Feldman was born on 8 July 1934 in the East End of London, the son of Jewish immigrants from Kiev, Ukraine, Cecilia (née Crook) and Myer Feldman, a gown manufacturer. He recalled his childhood as "solitary".

Feldman was married to Lauretta Sullivan (29 September 1935 – 12 March 2010) from January 1959 until his death in 1982. She died, aged 74, in Studio City, Los Angeles. Feldman's peers have reported, in a number of biographies, that he was highly attractive to women in spite of his unconventional facial appearance.

In 1954, Feldman first met Barry Took while both were working as performers, and with Took he eventually formed an enduring writing partnership which lasted until 1974. They wrote a few episodes of The Army Game (1960) and the bulk of Bootsie and Snudge (1960–62), both situation comedies made by Granada Television for the ITV network. For BBC radio they wrote Round the Horne (1964–67), their best-remembered comedy series, which starred Kenneth Horne and Kenneth Williams. (The last season of Round the Horne in 1968 was written by others.) This work placed Feldman and Took "in the front rank of comedy Writers," according to Denis Norden.

Feldman then became the chief Writer and script Editor on The Frost Report (1966–67). He co-wrote the much-shown "Class" Sketch with John Law, in which John Cleese, Ronnie Barker, and Ronnie Corbett faced the audience, with their descending order of height, suggesting their relative social status as upper class (Cleese), middle class (Barker), and working class (Corbett).

The television Sketch comedy series At Last the 1948 Show raised Feldman's profile as a performer. The other three participants, (future Pythons, Graham Chapman and John Cleese, and Future Goody, Tim Brooke-Taylor) needed a fourth cast member and had Feldman in mind. In a Sketch on 1 March 1967, Feldman's character harassed a patient shop assistant (played by Cleese) regarding a series of fictitious books, achieving success with Ethel the Aardvark Goes Quantity Surveying. His character in At Last the 1948 Show was often called Mr Pest, according to John Cleese. Feldman was co-author, along with Cleese, Chapman, and Brooke-Taylor of the "Four Yorkshiremen" Sketch, which was written for At Last the 1948 Show.

Feldman was given his own series on the BBC called Marty in 1968; it featured Brooke-Taylor, John Junkin, and Roland MacLeod, with Cleese as one of the Writers. Feldman won two BAFTA awards. The second series in 1969 was renamed It's Marty (the second title being retained for the DVD of the show)

During the course of his career, Feldman recorded one LP record, I Feel a Song Going Off (1969), re-released as The Crazy World of Marty Feldman. The songs were written by Denis King, John Junkin, and Bill Solly (a Writer for Max Bygraves and The Two Ronnies). It was re-released as a CD in 2007.

In 1971, Feldman gave evidence in favour of the defendants in the OZ trial. He would not swear on the Bible, choosing instead to affirm. Throughout his testimony, he mocked the judge after it was implied that he had no religion because he was not Christian. By this time, The Marty Feldman Comedy Machine (1971–1972) was in preparation, a TV series co-produced by Associated Television (ATV) and the American Broadcasting Company which was produced at ATV's Elstree Studios, near London. This show lasted for one season.

On film, in Mel Brooks' Young Frankenstein (1974), he was Igor (pronounced "EYE-gore", a comic response to Wilder's claim that "it's pronounced FRONK-EN-SCHTEEN"). Many lines in Young Frankenstein were improvised. Gene Wilder says 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 turns to the camera, points to his misaligned eyes with a grin and says, "Too late!"

In 1976, Feldman ventured into Italian cinema, starring with Barbara Bouchet in 40 gradi all'ombra del lenzuolo (Sex with a Smile), a sex comedy. He appeared in The Adventure of Sherlock Holmes' Smarter Brother and Brooks' Silent Movie, as well as directing and starring in The Last Remake of Beau Geste. He guest-starred in the "Arabian Nights" episode of The Muppet Show with several Sesame Street characters, especially Cookie Monster with whom he shared a playful cameo comparing their eyes side by side.

Feldman died from a heart attack in a hotel room in Mexico City on 2 December 1982 at age 48, during the making of the film Yellowbeard. On the DVD commentary of Young Frankenstein, Mel Brooks cites factors that may have contributed to Feldman's death: "He smoked sometimes half a carton (5 packs) of cigarettes daily, drank copious amounts of black coffee, and ate a diet rich in eggs and dairy products."

He is buried in Forest Lawn – Hollywood Hills Cemetery near his idol, Buster Keaton, in the Garden of Heritage.

Although his early performing career was undistinguished, he became part of a comedy act—Morris, Marty, and Mitch—that made its first television appearance on the BBC series Showcase in April 1955. Later in the decade, Feldman worked on the scripts for Educating Archie in both its radio and television incarnations with Ronald Chesney and Ronald Wolfe.