Sternhagen died peacefully of natural causes on Monday her son, John Carlin, said in a statement posted to Instagram on Wednesday.
"Fly on, Frannie," he wrote.
"The curtain goes down on a life so richly, passionately, humbly and generously lived."
Sternhagen's publicist confirmed the death and said it occurred in New Rochelle, New York.
Sternhagen won a Tony for best featured actress in a play in 1974 for her role in Neil Simon's The Good Doctor and a second one in 1995 for a revival of The Heiress." Her last turn on Broadway was in Seascape in 2005.
"I have been very fortunate," Sternhagen told the Daily Breeze of Torrance, California, in 2002.
"And I think a lot of that is because I'm considered a character actor — which really means you can do a variety of things. It doesn't mean that you can't do leading parts, because I have. But you're not limited to playing yourself."
In a 2005 review of Steel Magnolias, then-Associated Press drama critic Michael Kuchwara called Sternhagen "one of the treasures of New York theatre, able to invest any role she plays with considerable sympathy. Here, she turns what could be a throwaway part into one that provides much laughter — and applause."
She kept up a flourishing career while at the same time raising six children. She always said her family came first — commuting from her suburban home in New Rochelle while acting on Broadway — but admitted that touring and movie and TV work sometimes took her away from home.
"I remember telling my older daughter when she was about 13 that sometimes I felt terribly guilty that I wasn't home all the time," she said.
"And my daughter said, 'Oh, Mom, you would have been impossible if you were home all the time.' I'm sure she was right."
TV viewers knew her as played the rich grandmother of Dr. John Carter (Noah Wyle) in the long-running ER. On Cheers she was the know-it-all mother of postman Cliff Clavin (John Ratzenberger).
"She was just impossible and great fun to play," she told The New York Times. The role brought her two Emmy nominations.
More recently, she had a recurring role in Sex And The City as Bunny MacDougal, the strong-minded mother-in-law of Charlotte (Kristin Davis), which brought a third Emmy nomination, and played Kyra Sedgwick's mother in The Closer.
She met her husband, actor Thomas A Carlin, while appearing in a production in Maryland. He died of heart failure in 1991.
She and Carlin had four sons, Paul, Tony, Peter and John, and two daughters, Amanda and Sarah. She also is survived by nine grandchildren and two great-grandchildren.
