Henry was born to a Jewish family in New York City, the son of silent film Actress and star of the original Gentlemen Prefer Blondes, Ruth Taylor, and Paul Steinberg Zuckerman (April 15, 1899 – 1965), a retired Air Force brigadier general and stockbroker.

Henry attended The Choate School (now Choate Rosemary Hall) and Dartmouth College, where he met Bob Rafelson, and also worked on the Dartmouth Jack-O-Lantern humor magazine. From 1959 to 1962, as part of an elaborate hoax by Comedian Alan Abel, he pretended to be G. Clifford Prout, the quietly outraged President of the Society for Indecency to Naked Animals, who presented his point of view on talk shows.

Henry's dry humor attracted attention in the entertainment community. He became a cast member on TV programs such as The New Steve Allen Show (1961) and That Was The Week That Was (1964–65). He was a co-creator and Writer for Get Smart (1965–70), with Mel Brooks. Two of his TV projects had short runs but are fondly remembered by fans: Captain Nice (1967) with william Daniels as a reluctant superhero, and Quark (1978), with Richard Benjamin in command of a garbage scow in outer space. He also played Dr. Victor Rudman, a fractal scientist who dated Murphy, on the "My Dinner With Einstein" episode (1989) of Murphy Brown.

Henry hosted NBC's Saturday Night Live 12 times between 1976 and 1980. It became a tradition in those years for him to host the final show of each season. Henry also hosted the only live remote attempted by SNL, broadcast live from Mardi Gras in New Orleans. Henry's frequent host record would be broken when Steve Martin hosted the 14th season finale in 1989. During the October 30, 1976, episode, Buck Henry was injured in the forehead by John Belushi's katana in the samurai Sketch. Henry's head began to bleed and he was forced to wear a large bandage on his forehead for the rest of the show. As a gag, the members of the SNL cast each wore a bandage on their foreheads as well.

Henry has appeared in more than 40 films including The Graduate, Candy, Catch-22, Taking Off, The Man Who Fell to Earth, Gloria, Eating Raoul, Aria, Tune in Tomorrow, Defending Your Life, The Player, and Grumpy Old Men. He co-directed Heaven Can Wait, the 1978 remake of Here Comes Mr. Jordan, and appeared in the film as an officious angel, reprising the character originally played by Edward Everett Horton.

His many writing credits include Candy, The Owl and the Pussycat, What's Up, Doc?, Catch-22, The Day of the Dolphin, Protocol, and To Die For. He shared an Oscar nomination for his screenplay, The Graduate, a film in which he made a cameo appearance. In 1997, Henry was the recipient of the Austin Film Festival's Distinguished Screenwriter Award.

His Broadway credits include the 2002 revival of Morning's at Seven. Off-Broadway in July 2009, he starred opposite Holland Taylor in Mother, a play by Lisa Ebersole.

He appeared on the television show Will and Grace in 2005. In 2007, he made two guest appearances on The Daily Show as a contributor, billed as the show's "Senior Senior Correspondent". He has also appeared as Liz Lemon's father, Dick Lemon, in the 30 Rock episodes "Ludachristmas" (December 13, 2007) and "Gentleman's Intermission" (November 4, 2010). In 2011, he appeared in a multi-episode arc of Hot in Cleveland as Elka's groom.