McCann was born in Terenure in Dublin. His father was John J. McCann, a Playwright and Politician who served twice as Dublin's Lord Mayor. Although Donal had acted in a production of his father's Give Me a Bed of Roses at Terenure College in 1962, he briefly studied architecture before taking a job as a sub-editor at the Evening Press which allowed him pursue part-time acting classes at the Abbey School of Actors at the same time. He joined the Abbey Players in the late 1960s.

McCann began his film career early, in 1966, in Disney's The Fighting Prince of Donegal (this later became a TV series). More significant roles include the title character's father Shamie in Cal and one of the feuding brothers in Thaddeus O'Sullivan's December Bride (1990–1994). He has worked a number of times with Neil Jordan (in Angel, The Miracle and High Spirits).

McCann developed a particularly fruitful relationship with the Playwright Brian Friel. He played the role of Gar O'Donnell, the public figure, in a film adaptation of Philadelphia, Here I Come! in 1970 and, despite popular belief, he never played either public or private Gar on stage. He gave a landmark performance as Frank Hardy, the title character, in Faith Healer in 1980 (a role he reprised in 1994), continuing his relationship with Friel through productions of Translations (1988) and Wonderful Tennessee (1993).

On the London stage, McCann played in Prayer for My Daughter opposite Antony Sher (1978), and was Jean to Dame Helen Mirren's Julie in Miss Julie (1971). This was filmed for the BBC, and McCann would much later play Judge Brack with Fiona Shaw in the title role of Ibsen's Hedda Gabler, a production filmed for the BBC in 1993.

McCann played in Bob Quinn's Irish-language film Poitín (1979) and in Quinn's somewhat experimental The Bishop's Story (1995). After hearing that McCann was ill, Tom Collins asked Bob Quinn to make a TV documentary about McCann for RTÉ (in 1998) called It Must Be Done Right (after a remark by McCann on his craft). The film aired on RTÉ a week before McCann's death.

His career included parts in many plays from the Irish literary canon, including Tarry Flynn, The Shaughran, and the Gate Theatre's highly acclaimed production of Seán O'Casey's classic Juno and the Paycock in the 1980s (McCann played the "Paycock" (Captain Boyle) opposite Geraldine Plunkett as Juno and John Kavanagh as Joxer Daly) as well as a subsequent production of O'Casey's The Plough and the Stars.

His best-known film role was as Gabriel Conroy in The Dead (1987), starring opposite Anjelica Huston and directed by her father, John Huston. Significant late roles include Bernardo Bertolucci's Stealing Beauty (1996) and in John Turturro's Illuminata (released in 1999, after McCann's death).

Friel has said that McCann's work "contains extraordinary characteristics that go beyond acting ... it is deeply spiritual". Perhaps McCann's most renowned role was as Thomas Dunne in Sebastian Barry's The Steward of Christendom. He won the London Critics Circle Theatre Award (Drama Theatre) as best actor for this role in 1995. He reprised this role in a 1996 production at The Gate Theatre, Dublin and, following a twelve-week run at the Brooklyn Academy of Music in 1997, his "performance of unarguable greatness" (New York Observer) had Newsweek hailing him as "a world-class star", and The New York Times referring to this "astonishing Irish actor...widely regarded as the finest of them all".