He close friend Bishop William Frey told CNN that Davis slipped on her bathroom floor, knocked her head and suffered a subdural hematoma. She never regained consciousness.
Nelson's death was a "shock" to her friends, who described her as healthy and active.
Davis, a University of Michigan graduate, worked in television since the 1950s. She went on to win two Emmy Awards for her work as secretary Schultzy on The Bob Cummings Show, before landing at The Brady Bunch in 1969.
She played Alice Nelson, the Brady family's joke-telling housekeeper, until 1974. She reprised her role in several Brady Bunch movies, including 1981's The Brady Brides and 1995's The Brady Bunch Movie.
Davis spoke about her characterization of Alice in a 2004 interview.
"I cared very much about this family, it was my family. I would die for every single one of them," she said of Alice.