Malcolm, who was born in Aberdeen but grew up in Canada, enjoyed a career that spanned stage and screen. He starred in the original theatre production of Richard O'Brien's The Rocky Horror Show in 1974, appeared in Star Wars Episode V and was a familiar face to fans of sitcom Absolutely Fabulous, in which he appeared as Saffy's father.
His daughter, Morgan Lloyd Malcolm, announced his death via Twitter, saying that the world had lost a "beautiful, brilliant man". She added: "My dad Christopher Malcolm left peacefully and with dignity. He will always be my hero."
Malcolm also starred in films such as Highlander and Labyrinth but he continued to work in theatre, co-producing a revival of the Rocky Horrow Show in the West End.
His latest project, a revival of Oh What a Lovely War, opened at the Theatre Royal Stratford East at the start of this month.
The theatre said it was a "very sad day", adding: "He is deeply missed."
After his daughter was inundated with messages of condolence, she replied: "So touched and moved by the wonderful messages and tweets about my dad. He was such a special guy. I'm so happy others have such memories too."
Malcolm, who died on Saturday, is survived by his wife Judy Lloyd, his three children and a grandson.