Thompson, 83, died Wednesday from lung disease, her daughter Liza Sguaglia told The New York Times.
Thompson made her name in the 1950s as off-Broadway came into prominence. She appeared in plays such as "The Misanthrope" and Chekhov's "Ivanov."
She won a Tony in 1972 for playing four different parts -- three daughters and their elderly mother -- in four vignettes constituting George Furth's "Twigs."
She also played roles in numerous television productions, most notably as Kate Lawrence in a show called "Family."
She was nominated for an Emmy four times in the show's five seasons, winning in 1978.
Thompson was born in Des Moines, Iowa, on Sept. 27, 1927. She graduated with a drama degree from the Carnegie Institute of Technology in Pittsburgh, now Carnegie Mellon University. She married Donald Stewart.
Besides her husband and daughter, Thompson is survived by a brother, David.