Davis fell in her bathroom early Sunday morning and never regained consciousness, the couple she lived with told TMZ. Her death was a "total shock," as she had been in good health for her age, they added.
Born in Schenectady, New York, Davis graduated from the University of Michigan at Ann Arbor in 1946 with a degree in drama and speech, despite starting out as a pre-med student.
In the late 1950s, she starred on The Bob Cummings Show as Charmaine "Schultzy" Schultz, and received two Emmy Awards for Outstanding Supporting Actress in a Comedy Series for the role. (She was nominated four times.) She received a star on the Hollywood Walk of Fame in 1960.
Davis is best known for playing Alice on The Brady Bunch from 1969 to 1974, as well as resurrecting the part for subsequent movies and TV specials. She most recently reunited with the rest of the show's surviving cast members for a 2004 TV Land special celebrating the series' 35th anniversary.
Davis's other television credits include The John Forsythe Show, on which she played Miss Wilson. She never officially retired from acting, and in recent years had starred in commercials for Swiffer and Shake 'n' Bake.