The American-English phrase where’s your violin? is said to a man to mean you need a haircut.

It originated in the conventional image of male musicians wearing their hair long.

For example, in Lock, stock, and sideburns, published in The Guardian (Manchester, Lancashire, England) of Wednesday 17^th August 1966, the U.S. journalist, author and critic Stanley Reynolds (1934-2016) wrote of the day he decided to have a haircut for the first time in six months, and mused “on the difficulties and distresses [his] own style d’autrefois had occasioned”:

A judge in New England where I was reporting his court told me privily to get a haircut: “How can I scream and shout at these thugs and order them haircuts as punishment for hitting one another with bicycle chains, if you sit in this court looking like Shirley Temple?” And you had the complete stranger who would accost you asking where your violin was. Or call you Einstein or Beethoven.

The earliest occurrence of the phrase that I have found is from No Toughs Wanted, by Virginia Gardner, published in The Daily Oklahoman (Oklahoma City, Oklahoma) of Sunday 20^th January 1929:

The picturesque, hardened messenger boy, who prided himself on being “tough,” who played with such complete indifference his role in the tragedies and farces of life in a city, is a ghost of the past.
An ambitious lad who is taught by his bosses to look upon the job of messenger as a stepping stone to a business career, replaces the once-familiar messenger boy whose cynicism embraced life in general and whose ambition was confined to the ability to lick any of the other boys at a moment’s notice.
The “uplift” of the messenger boy has been accomplished by the telegraph companies, and in Oklahoma City, in co-operation with the mothers of the boys, with whom Ray E. Miller, manager of a delivery department, keeps in touch, and with the co-operation of heads of civic, business, church and welfare organizations.
[…]
When the company had its office here back in frontier days, first at 104 West Main street, then at 28 Main street in the old Lee hotel, and later, in 1902, at 19 Broadway, “uniforms” of the messenger boys, then employed by the American District Telegraph, were of a mongrel variety.
In those days, it was an integral part of his professional appearance for a messenger lo look slouchy and more or less informal.
Not so today. “Caps squarely on the head,” is one of the sacred commandments of the modern messenger boy. “Hair trimmed” is another, “coat buttoned top to bottom,” “clean hands and face,” “sleeves correct length,” and “high top shoes polished” are others.
Every night before a boy goes off duty he must use elbow grease and the electric shiner on his puttees and his shoes.
Every morning he must stand at attention in the confines of a while circle marked on the floor outside the messengers’ room and stand rigorous inspection.
“Well, where is your violin?” Miller may say to a “green” boy.
“What, sir?”
“Aren’t you planning to be a violinist, then? Well, you might as well get your hair cut.”

The second-earliest occurrence of the phrase that I have found is from the column Up and Down the Boulevard, by Potter B. Brayton, published in The Wisconsin State Journal (Madison, Wisconsin) of Sunday 27^th April 1930—Johnny Mack Brown (1904-1974) was a U.S. film actor:

I witnessed the most dazzling premiere Hollywood has had in several months at the Carthay Circle theater last night. Universal’s “All Quiet on the Western Front” was the picture having its debut. […]
[…]
Freeman Lang, nonpareil of preview wise-crackers, was personally responsible for about 50 per cent of the premiere’s success. I never saw a master of ceremonies instill such a “clubby-little-family-gathering” spirit into both celebrities and audience!
[…]
Johnny Mack Brown was too aware of the incongruity of his long curls and full dress suit to present his usual dignity. He is letting his hair grow for a forthcoming production, and was considerably fussed when Freeman Lang asked in his jovial booming voice, “Where’s your violin, Johnny?”

According to Nat Shapiro in An Encyclopedia of Quotations about Music (New York: Da Capo Press, Inc., 1981), the Reader’s Digest of May 1938 attributed the following to the U.S. statesman Franklin Delano Roosevelt (1882-1945):

It got to a point where I had to get a haircut or a violin.

Niccolò Paganini (1782-1840), Italian violinist, violist, guitarist and composer—from The Sphere (London, England) of Saturday 18^th January 1930: