Plowright was born in Brigg, Lincolnshire to Daisy Margaret Burton and William Ernest Plowright, a journalist and newspaper editor. She attended Scunthorpe Grammar School and trained at the Bristol Old Vic Theatre School.

Long known as a superb theatre actress, Plowright made her stage debut in 1951 and her London debut in 1954. In 1956 she joined the English Stage Company at the Royal Court and won the role of Margery Pinchwife in The Country Wife. She appeared with George Devine in the Eugène Ionesco paly, Les Chaises, Major Barbara, Saint Joan, and in 1957 she co-starred with future husband Sir Laurence Olivier in the original London production of John Osborne's The Entertainer, taking over the role of Jean Rice from Dorothy Tutin when the play transferred from the Royal Court to the Palace Theatre.

Plowright continued to appear on stage and in films such as The Entertainer (1960) and The Three Sisters (1970). In 1961 she received a Tony Award for her role in A Taste of Honey on Broadway. After a brief hiatus to devote time to her family she has returned to the screen and can be seen in films such as Dennis the Menace, Enchanted April and Tea With Mussolini. She was also notable for her major role in 101 Dalmatians.

In 2003 Plowright performed in the stage production Absolutely! in London.

Plowright was first married to Roger Gage. She divorced him, and, in 1961 married Laurence Olivier. Together the couple had three children, Richard Kerr, Tamsin Agnes Margaret and Julie-Kate. Both daughters are actresses . The couple were married until his death from cancer in 1989. Her brother, David Plowright, once an executive at Granada Television, was awarded a knighthood in the 2004 New Year's Honours together with Dame Joan.

The Plowright Theatre in Scunthorpe, North Lincolnshire, is named in her honour. Upon her marriage to Sir Laurence Olivier, her formal title became "Lady Olivier", however, it is not used in her professional career.