Born David Daniel Kaminsky to Ukrainian Jewish immigrants in Brooklyn named Jacob Kaminsky (father) and Clara Kaminsky (mother), Kaye became one of the world's best-known comedians. He spent his early youth attending Public School 149 in East New York, Brooklyn, before moving to Thomas Jefferson High School, but he never graduated. He learned his trade in his teenage years in the Catskills as a tummler in the Borscht Belt.

Danny Kaye made his film debut in a 1935 comedy short titled Moon Over Manhattan. In 1937 he signed with New York–based Educational Pictures for a series of two-reel comedies. Kaye usually played a manic, dark-haired, fast-talking Russian in these low-budget shorts, opposite young hopefuls June Allyson or Imogene Coca. The Kaye series ended abruptly when the studio shut down permanently in 1938.

Kaye scored a personal triumph in 1941, in the hit Broadway comedy Lady in the Dark. His show-stopping number was "Tchaikovsky", by Kurt Weill and Ira Gershwin, in which he sang the names of a whole string of Russian composers at breakneck speed, seemingly without taking a breath.

His feature film debut was in producer Samuel Goldwyn's Technicolor 1944 comedy Up in Arms, a remake of Goldwyn's Eddie Cantor comedy Whoopee! (1930). Goldwyn agonized over Kaye's ethnic, Borscht-belt looks and ordered him to undergo a nose job. Kaye refused, and Goldwyn found another way to brighten Kaye's dark features by lightening his hair, giving him his trademark redheaded locks. Kaye's rubber face and fast patter were an instant hit, and rival producer Robert M. Savini cashed in almost immediately by compiling three of Kaye's old Educational Pictures shorts into a makeshift feature, The Birth of a Star (1945).

Kaye starred in several movies with actress Virginia Mayo in the 1940s, and is well known for his roles in films such as The Secret Life of Walter Mitty (1947), The Inspector General (1949), On the Riviera (1951) co-starring Gene Tierney, White Christmas (1954, in a role originally intended for Fred Astaire, then Donald O'Connor), Knock on Wood (1954), The Court Jester (1956), and Merry Andrew (1958). Kaye starred in two pictures based on biographies, Hans Christian Andersen (1952) about the Danish story-teller, and The Five Pennies (1959) about jazz pioneer Red Nichols. His wife, writer/lyricist Sylvia Fine, wrote many of the witty, tongue-twisting songs Danny Kaye became famous for. Some of Kaye's films included the theme of doubles, two people who look identical (both played by Danny Kaye) being mistaken for each other, to comic effect. The Kaye-Fine marriage, as was the case with many spouses who worked together in the high-pressure world of film-making, was sometimes stormy.

During World War II, the Federal Bureau of Investigation investigated rumors that Kaye dodged the draft by manufacturing a medical condition to gain 4-F status and exemption from military service. FBI files show he was also under investigation for supposed links with Communist groups. The allegations were never substantiated, and he was never charged with any associated crime.

Kaye starred in a radio program of his own, The Danny Kaye Show, on CBS in 1945–1946. Although it had a stellar cast (including Eve Arden, Lionel Stander, and Big Band leader Harry James), and was scripted by radio notables Goodman Ace, Sylvia Fine, and respected playwright-director Abe Burrows, the show failed to make proper use of its star, and never found an audience. It turned out to be a very bitter experience for both Kaye and Ace. Many episodes survive today, and are notable for Kaye's opening "nonsense" patter.

Kaye was sufficiently popular that he inspired imitations:

When he appeared at the London Palladium music hall in 1948, he "roused the Royal family to shrieks of laughter and was the first of many performers who have turned English variety into an American preserve." Life magazine described his reception as "worshipful hysteria" and noted that the royal family, for the first time in history, left the royal box to see the show from the front row of the orchestra.

He hosted the 24th Academy Awards in 1952. The program was broadcast only on radio. Telecasts of the Oscar ceremony would come later.