Shaw was born Irwin Gilbert Shamforoff in the South Bronx, New York City, to Russian Jewish immigrants. His parents were Rose and Will. His younger brother, David Shaw, became a noted Hollywood Producer and Writer. Shortly after Irwin's birth, the Shamforoffs moved to Brooklyn. Irwin changed his surname upon entering college. He spent most of his youth in Brooklyn, where he graduated from Brooklyn College with a Bachelor of Arts degree in 1934.

Shaw began screenwriting in 1935 at the age of 21, and scripted for several radio shows, including Dick Tracy, The Gumps and Studio One. He recaptured this period of his life in his short story "Main Currents of American Thought," about a hack radio Writer grinding out one script after another while calculating the number of words equal to the rent money:

Shaw summered at the Pine Brook Country Club, located in the countryside of Nichols, Connecticut, which became the 1936 summer home of the Group Theatre (New York), whose roster included Elia Kazan, Harold Clurman, Harry Morgan, John Garfield, Frances Farmer, Will Geer, Clifford Odets and Lee J. Cobb.

During the 1940s, Shaw wrote for a number of films, including The Talk of the Town (a comedy about civil liberties), The Commandos Strike at Dawn (based on a C.S. Forester story about commandos in occupied Norway) and Easy Living (about a football player unable to enter the game due to a medical condition). Shaw married Marian Edwards (daughter of well-known screen actor Snitz Edwards). They had one son, Adam Shaw, born in 1950, himself a Writer of magazine articles and non-fiction.

The Young Lions, Shaw's first novel, was published in 1948. Based on his experiences in Europe during the war, the novel was very successful and was adapted into a 1958 film. Shaw was not happy with the film.

In 1950, Shaw wrote a book on Israel with photos by Robert Capa named Report on Israel.

Shaw's second novel, The Troubled Air, chronicling the rise of McCarthyism, was published in 1951. He was among those who signed a petition asking the U.S. Supreme Court to review the John Howard Lawson and Dalton Trumbo convictions for contempt of Congress, resulting from hearings by the House Committee on Un-American Activities. Accused of being a communist by the Red Channels publication, Shaw was placed on the Hollywood blacklist by the movie studio bosses. In 1951 he left the United States and went to Europe, where he lived for 25 years, mostly in Paris and Switzerland. He later claimed that the blacklist "only glancingly bruised" his career. During the 1950s he wrote several more screenplays, including Desire Under the Elms (based on Eugene O'Neill's play) and Fire Down Below (about a tramp boat in the Caribbean).

While living in Europe, Shaw wrote more bestselling books, notably Lucy Crown (1956), Two Weeks in Another Town (1960), Rich Man, Poor Man (1970) (for which he would later write a less successful sequel entitled Beggarman, Thief) and Evening in Byzantium (made into a 1978 TV movie). Rich Man, Poor Man was adapted into a highly successful ABC television miniseries in 1976.

His novel The Top of the Hill was made into a TV movie about the Winter Olympics at Lake Placid in 1980, starring Wayne Rogers, Adrienne Barbeau, and Sonny Bono.

Shaw was highly regarded as a short story author, contributing to Collier's, Esquire, The New Yorker, Playboy, The Saturday Evening Post, and other magazines; and 63 of his best stories were collected in Short Stories: Five Decades (Delacorte, 1978), reprinted in 2000 as a 784-page University of Chicago Press paperback. Among his noted short stories are: "Sailor Off The Bremen", "The Eighty-Yard Run", and "Tip On A Dead Jockey". Three of his stories ("The Girls in Their Summer Dresses", "The Monument", "The Man Who Married a French Wife") were dramatized for the PBS series Great Performances. Telecast on June 1, 1981. This production was released on DVD in 2002 by Kultur Video.

Shaw died in Davos, Switzerland on May 16, 1984, aged 71, after undergoing treatment for prostate cancer.