Saint-Denis was born in Beauvais, the nephew of Jacques Copeau, who had founded the Théâtre du Vieux-Colombier in 1913.
Saint-Denis was greatly influenced by Copeau's approach to theatre taught at his Ecole du Vieux-Colombier, which embraced not only the play on stage but also the actor training itself.
Working together with established actors like Alec Guinness, Peter Ustinov, Michael Redgrave, John Gielgud or Laurence Olivier, he soon became known as a renowned director.
In 1961 he was named artistic advisor at the new Royal Shakespeare Company, and in 1966 he appeared as a storyteller on the BBC children's programme Jackanory narrating in five episodes.
Having suffered from health problems for a long time, Michel Saint-Denis died in Westminster from a stroke, aged 73.