Massey was born in Thakeham, Sussex, England, the daughter of British actress Adrianne Allen and Canadian-born Hollywood actor Raymond Massey. Her brother, Daniel Massey, was also an actor. She was the niece of Vincent Massey, a Governor General of Canada, and her godfather was film director John Ford. Although she had no formal training at either drama school or in repertory, in May 1955 at the age of 17, Anna Massey made her first appearance on stage at the Theatre Royal, Brighton, as Jane in The Reluctant Debutante, subsequently making her first London appearance in the same play at the Cambridge Theatre in May 1955 “and was suddenly famous”. She then left the cast in London to repeat her performance in New York in October 1956. In the 1990s she appeared with Alan Bennett in a dramatised reading of T.S. Eliot’s and Virginia Woolf’s letters in a production at the Charleston Festival devised by Patrick Garland. Several of her early film roles were in mystery thrillers. She made her cinema debut in the Scotland Yard film Gideon’s Day (1958), as Sally, daughter of Jack Hawkins’s Detective Inspector. The director was her godfather John Ford. She played a potential murder victim in Michael Powell’s cult thriller Peeping Tom (1960) and appeared in Otto Preminger’s Bunny Lake Is Missing (1965). In 1972, she played the role of the barmaid Babs in Alfred Hitchcock’s penultimate film Frenzy. In the documentary on the film’s DVD release, Massey mentioned that she originally auditioned for the much smaller role of the secretary Monica, a part for which Jean Marsh was cast. She also noted that her character’s nude scenes in Frenzy were performed by body doubles. Massey appeared with her brother Daniel playing deadly siblings in the horror film The Vault of Horror (1973).

Massey continued to make occasional film and stage appearances, but worked more frequently in television, making her first small screen appearance as Jacqueline in Green of the Year in October 1955 and in dramas such as The Pallisers (1974), the 1978 adaptation of Rebecca (in which she starred with her ex-husband, Jeremy Brett), The Mayor of Casterbridge (1978), The Cherry Orchard (1980), and Anna Karenina (1985). She had roles in the British comedy series The Darling Buds of May (1991) and The Robinsons (2005). She also appeared in a number of mysteries and thrillers on television, including episodes of Inspector Morse, The Inspector Alleyn Mysteries, Midsomer Murders, Strange, Lewis, and Agatha Christie’s Poirot. With Imelda Staunton, she co-devised and starred as Josephine Daunt in Daunt and Dervish on BBC radio. She was the narrator of This Sceptred Isle on BBC Radio 4, a history of Britain from Roman times which ran for more than 300 fifteen-minute episodes. In 2009, she also appeared in a new radio version of The Killing of Sister George. In 1987, Massey was awarded the British Academy TV Award for Best Actress for her role in Hotel du Lac  after acquiring the TV rights two years earlier, only a few weeks before the novel won the Booker Prize. She also appeared as Mrs. D’Urberville in the 2008 BBC adaptation of Tess of the D’Urbervilles, an older version of May and as Rosie in An Angel For May, and in the 2004 BBC version of Our Mutual Friend.

In the New Year’s Honours List published 31 December 2004 she was created a Commander of the Order of the British Empire (CBE) for services to drama. Massey published an autobiography in 2006, Telling Some Tales, in which she revealed a difficult early life and discussed her failed marriage (1958–1962) to actor Jeremy Brett, discussing his struggle with bipolar disorder. The couple had one son, writer and illustrator David Huggins (b. 1959). At an August 1988 dinner party held at the home of their mutual friend, Joy Whitby, she met Russian-born metallurgist Uri Andres, who had been based at Imperial College, London since 1975. The couple were married from November 1988 until her death in 2011. Massey was quoted as saying, “Theatre eats up too much of your family life. I have a grandson and a husband and I’d rather I was able to be a granny and a wife.” Massey died from cancer on 3 July 2011, aged 73. She is survived by her son, grandson and second husband.