The noun monokini denotes a woman’s topless swimsuit, consisting of the lower half of a bikini.

This noun is from the prefix mono-, meaning one, once, and -kini in bikini, reinterpreted as containing the prefix bi-, meaning two, twice.

It is generally claimed that the noun monokini was coined in 1964 by the Austrian-born U.S. fashion designer Rudolf ‘Rudi’ Gernreich (1922-1985).

But, as I have explained in refutation of received ideas on the origin of ‘bikini’, both the nouns bikini and monokini were in fact coined in 1946 by the French automobile engineer and clothing designer Louis Réard (1897-1984). The following is from Femmes d’Aujourd’hui (Today’s Women – no 1419 – Bruxelles, Belgium) of Wednesday 12^th July 1972:

Dans un récent shopping maillots de bain (no 1411 du 17 mai), nous avons, par distraction, utilisé le mot « Bikini » comme synonyme de « deux pièces ». A la suite de ce « lapsus », on nous communique : « La Maison Réard, 9, avenue de l’Opéra, Paris, spécialiste des maillots de bain une pièce et deux pièces, rappelle qu’il est absolument interdit de se servir du terme Bikini ou de ses dérivés pour désigner un article quelconque qui ne soit pas de sa propre fabrication. En effet, Bikini et ses dérivés tels que Monokini, Sexykini, etc., sont des marques déposées dans de nombreuses classes par Louis Réard, le 20 juin 1946, sous le no 368.289 au Greffe du Tribunal de la Seine. Il en est donc le seul et unique propriétaire n’ayant jamais accordé de licence à quiconque. »
     translation:
In a recent swimwear shopping section (no 1411 of 17^th May), we inadvertently used the word “Bikini” as a synonym for “two-piece swimming costume”. Following this “lapsus”, we have received this communication: “The Maison Réard, 9, avenue of the Opera, Paris, specialists in one-piece and two-piece swimming costumes, remind that it is absolutely forbidden to use the term Bikini or its derivatives to designate any article that is not of their own fabrication. As a matter of fact, Bikini and its derivatives such as Monokini, Sexykini, etc., are trademarks registered in numerous classes by Louis Réard, on 20^th June 1946, under the no 368.289 at the Clerk’s Office of the Tribunal of the Seine Department.  He is therefore the sole and unique proprietor of them having never granted licence to anyone.”

However, the earliest English uses of the noun monokini that I have found date from 1964—they are as follows, in chronological order:

1-: From a UPI (United Press International) story published in many newspapers on Sunday 28^th June 1964—for example in The Cincinnati Enquirer (Cincinnati, Ohio, USA):

LONDON (UPI)—The bare bosom fashion craze in Europe has switched from women’s dresses to bathing suits and some beaches on the continent are starting to look like Paris strip-tease shows.
Despite the increasing popularity in [sic] the “monokini”—or one-piece bikini—a leading German swimsuit manufacturer of topless bathing suits warned, “women who cannot wear them will see to it that [those] who can won’t.”
Although the bare bosoms are frequently seen on the Riviera, where pretty girls casaully [sic] take off their bikini tops to get a little sun, the topless bathing suit craze has created quite a stir in Europe, as well as the United States.
Italian actress Gina Lollobrigida apparently summed up the argument against them when she said, “they lack taste and intelligence. They lack taste because they are esthetically questionable, and intelligence because it is unwise to destroy that atmosphere of reserve and mystery that is one of the secrets of feminine charms.
“I am sure they will not last more than one season. Next year we will already have forgotten them.”
Claudia Cardinale, another Italian film beauty, put it another way: “They are esthetically horrible. They destroy the silhouette. They are decidedly unfeminine.”
The bare bosom craze received its first boost in Europe a week ago when Rae Southern, one of the leading dancers at Raymond’s Revue Bar, a London nightclub, strolled into the Capri Restaurant wearing a topless evening gown.
Miss Southern, a beautiful blonde, wore the gown to win a five-pound ($14) bet from her boss, Paul Raymond, who said she “didn’t have the guts to wear such a dress.”
“When I took off my fur in the restaurant there were about seven other people there,” Miss Southern said. “They took quick looks and then kept their eyes elsewhere. But later the manager very politely asked me to leave. He said I was causing embarrassment to his clients.
“But proof that not all men were embarrassed is the fact that the waiter who served me in the restaurant didn’t bat an eyelid when he took our order.”
Although the topless dress did not set the fashion world afire, it fired the imagination of bathing suit designers and the topless swim suit went on display throughout Europe.
Most men are in favor of “monokinis.” A typical comment from one was: “Because of civilization women are no longer natural. In many places in Africa it is indecent to cover the breasts.”
In France, England and Denmark, officials either turned a blind eye to bare-bosomed beach girls or gave formal approval to the controversial new style.
In London, a borough council in suburban West Ham ruled it would permit topless swimsuits in local swimming pools—but only at women-only sessions.
“We’re not narrow-minded,” Councillor Mrs. Alice Gannon said. “If the craze catches on and people want to swim partially nude, I don’t see why we should stop them. As long as they don’t upset other swimmers, then everything is okay.”
The latest wrinkle in the topless trend is the “strip-tease dress,” marketed by a London firm. The company said the dress is convertible. Detachable panels cover the bust.
Depending upon the occasion, the wearer can:
● Button the neckline up to the throat.
● Drop the neckline below the legal limit.
● Expose one breast completely, leaving the other covered.
“Our dress is daring without being indecent,” designer Cyrill Bier said. “You could do a slow strip-tease in it during the evening without going the whole hog. Half a bust is far more seductive than complete exposure. It leaves something to the imagination.”

2-: From an AP (Associated Press) story published in many newspapers on Wednesday 1^st July 1964—for example in The Albuquerque Tribune (Albuquerque, New Mexico, USA):

EL PASO, Tex., July 1 (AP)—The topless bikini has been given the title of “monokini” by Mexican newsmen.
Blaring eight-column headlines in a Tuesday newspaper in Juarez, Mexico, said the monokini had made a “scandalous invasion of Mexico.”
The term monokini was arrived at by the following logic:
A “bi-kini” means two-piece, so therefore the new invention should appropriately be called “mono-kini” because it is only one piece.

3-: From The Detroit Free Press (Detroit, Michigan, USA) of Wednesday 1^st July 1964:

Swedes Bare Bosom Contest

In Malmoe, Sweden, several local girls have announced they will compete in the world’s first Miss Bare Bosom contest there.
The contest, organized by a local restaurateur, has run into some difficulty, however.
A local newspaper has refused to print an advertisement for the event announcing that the “most beautiful bosom will be crowned.”
The organizer says contestants will dress in “monokinis”—one-piece bikinis—and in topless evening gowns for separate judgings.
MEANWHILE, at Goteburg, a student club announced a dance Tuesday night to which girls wearing topless evening dresses will be admitted free.
And the bare-bosom fashion was banned Tuesday in a number of British cities, but a 17-year-old African beauty welcomed the fad as “an important step in the white woman’s social progress.”
“It is high time our civilization spread also to white women,” Deolinda Ferreira said after a bare-bosomed jungle dance at her home village in Zavala, Mozambique.
Topless bathing suits for women were banned by the town corporation in Eastbourne, England, under a bylaw which says that “at all times females shall wear dresses reaching from the neck down to the ankles.”
A British organization known as the Guild of Lady drivers said in a message to its members that topless dresses should not be worn on any motoring occasion because they are uncomfortable and dangerous.
DR. MICHAEL Ramsey, the Archbishop of Canterbury, said any Christian “should express his disgust at anything he sees indecent, but short of that the less disapproval he expresses the better.”

4-: From The Modesto Bee and News-Herald (Modesto, California, USA) of Thursday 2^nd July 1964:

Wear A Monokini To Get Tops In Service

NORWICH, Conn.—AP—Talk about service!
Attendants at a gasoline station just could not do enough for the driver of a sedan yesterday.
The oil was checked, the battery serviced, the tires inflated, the floors swept, the windows—especially the windshield—were polished with great care.
The driver was a young woman . . . in a topless bathing suit.