Feldman was born in London's East End, the son of Jewish immigrants from Kiev. His memory of childhood is that it was a solitary experience. Leaving school at 15, he worked at the Dreamland fun fair in Margate. By the age of 20 he had decided to pursue a career as a comedian.

In 1954, Feldman formed a writing partnership with Barry Took. For British television, they wrote situation comedies such as The Army Game, Bootsie and Snudge, and most notably the ground-breaking BBC radio show Round the Horne, which starred Kenneth Horne and Kenneth Williams. This put Feldman and Took "in the front rank of comedy writers" (Dennis Norden).

The television sketch comedy series At Last the 1948 Show featured Feldman's first on-screen performances. The other three performers realised they needed a fourth to complete the group and Brooke-Taylor and Cleese both had Feldman in mind when they discussed completing the group in a phone call.. In one sketch first broadcast on 1 March 1967, Feldman harassed a patient shop assistant (John Cleese) for a series of fictitious books, finally achieving success with Ethel the Aardvark Goes Quantity Surveying. The sketch was revived as part of the Monty Python stage show repertoire, and on Monty Python's Contractual Obligation Album (both without Feldman).

Marty Feldman was co-author, with John Cleese, Graham Chapman and Tim Brooke-Taylor, of the "Four Yorkshiremen" sketch, which was also written for At Last the 1948 Show. The "Four Yorkshiremen" sketch was performed during Amnesty International concerts (by members of Monty Python, once including Rowan Atkinson in place of Python member Eric Idle), as well as during Monty Python Live at the Hollywood Bowl and other Monty Python shows and record albums.

This has led to the "Four Yorkshiremen" sketch now being considered a Monty Python sketch, with the origin and co-authorship of the sketch by non-Monty Python writers Marty Feldman and Tim Brooke-Taylor being overlooked or forgotten by many people. Feldman was also script editor on The Frost Report with several future members of Monty Python. He wrote the famous "Class" sketch wherein Cleese, Ronnie Barker and Ronnie Corbett stand facing the audience in descending order of height declaring their social status.

Following his success on At Last the 1948 Show, Feldman had a series of his own on the BBC called Marty (1968), which also featured Tim Brooke-Taylor, John Junkin and Roland MacLeod with Cleese on board in a writing capacity. Feldman won two BAFTA awards for the show. The second series (made in 1969) was renamed It's Marty (with the second title being retained for the DVD release of the show); in 1972 he switched to the ITV station ATV for one series before returning to the BBC.

In 1974, Dennis Main Wilson (producer for the UK television show Till Death Us Do Part) produced a short sketch series for Feldman entitled Marty Back Together Again, a reference to reports about the star's health. But this series never recaptured the impact of the earlier series. The Marty series proved popular enough with an international audience (the first series won the Golden Rose Award at Montreaux) to launch a film career. His first feature role was in 1970's Every Home Should Have One which is remembered only by serious students of comedy or completists.

Marty Feldman's performances on American television included The Dean Martin Show and Marty Feldman's Comedy Machine. On film, he is best remembered for his role as Igor (pronounced "EYE-gore") in Young Frankenstein where many of his lines were improvised. Gene Wilder says that he had Feldman in mind when he wrote the part. At one point, Dr. Frankenstein (Wilder) scolds Igor with the phrase "Damn your eyes!" Feldman then turns to the camera, points to his already-misaligned eyes, grins and says, "Too late!"

Feldman met American comedy writer Alan Spencer on the set of Young Frankenstein when Spencer was a teenager. Spencer was a devout fan of Feldman as both a writer and performer. Feldman took Spencer under his wing and offered him key guidance that eventually led the young scribe to create the television show Sledge Hammer!.

Feldman died from a heart attack in a hotel room in Mexico City, Mexico during the making of the film Yellowbeard. Cartoonist Sergio Aragonés was filming a movie nearby and when he introduced himself to Feldman earlier that night, he frightened Feldman and possibly induced his heart attack. Aragones was dressed for his role in the film as an armed police officer. He ran up to Feldman, apparently startling him. He has told the story with the punchline "I killed Marty Feldman".