The actress, who play divorced mom Ann Romano on the long-running sitcom, passed away at her home due to complications from pancreatic cancer, family members said in a statement.
Her family had announced she was diagnosed with cancer in September.
Franklin was a veteran stage and television performer before One Day At A Time made her a star.
Screen legend: Veteran stage and TV actress Bonnie Franklin, pictured in 2012, passed away Friday due to complications from pancreatic cancer, said her family
It premiered on CBS in December 1975, just five years after the network had balked at having Mary Tyler Moore play a divorcee on her own comedy series, insisting that newly single Mary Richards be portrayed as having ended her engagement instead.
On her own in Indianapolis, Ann Romano was raising two teenage girls (played by Mackenzie Phillips, already famous for the film American Graffiti, and a previously unknown Valerie Bertinelli).
Groundbreaking: The actress, pictured in 2011, was famous for playing a divorced mother on the sitcom One Day At A Time
'The years on One Day at a Time were some of the happiest of my life, and along with Pat [Harrington Jr.] and Mackenzie [Phillips] we were a family in every way.
'She taught me how to navigate this business and life itself with grace and humor, and to always be true to yourself. I will miss her terribly.'
Single matriarch: Franklin broke new ground with her character in the sitcom, about a young divorced mother seeking independence from her suffocating marriageOne Day At A Time ran on CBS until 1984, by which time both daughters had grown and married, while Romano had remarried and become a grandmother. During the first seven of its nine seasons on the air, the show was a Top 20 hit.
Like other Lear productions such as All In The Family and Good Times, One Day at a Time dealt with contemporary issues once absent from TV comedies such as premarital sex, birth control, suicide and sexual harassment - issues that had previously been overlooked by TV comedies whose households were usually headed by a husband and wife or, rarely, a widowed parent.
Meanwhile, the series weathered its own crises as Phillips was twice written out of the series to deal with her drug abuse and other personal problems.
It's a hit: One Day At A Time ran on CBS until 1984, by which time both daughters had grown and married, while Romano had remarried and become a grandmother. During the first seven of its nine seasons on the air, the show was a Top 20 hit.
In her 2008 memoir Losing It, Bertinelli noted that Franklin, just 31 when the show began, wasn't old enough to be her real mother.
Even so, wrote Bertinelli, 'within a few days I recognized her immense talent and felt privileged to work with her. ... She was like a hip, younger complement to my real mom.'
Like old times: Franklin appeared in an episode of Hot In Cleveland in 2011 with her on-screen daughter from One Day At A Time Valerie Bertinelli
Franklin herself was married for 29 years. Her husband, TV producer Marvin Minoff, died in 2009.
Born Bonnie Gail Franklin in Santa Monica, California, she entered show business at an early age. She was a child tap dancer and actress, and a protege of Donald O'Connor, with whom she performed in the 1950s on NBC's Colgate Comedy Hour.
A decade later, she was appearing on such episodic programs as Mr. Novak, Gidge and The Man From U.N.C.L.E.
Long-running career: The California native entered show business at an early age as a child actress and tap dancer
Franklin's recent credits include appearances on The Young And The Restless and the TV Land comedy Hot in Cleveland, which again reunited her with Bertinelli, one of that show's regulars.
A private memorial will be held next week, her family said.