Bandmate Peter Yarrow said Travers handled her disease with "great dignity."
"It was, as Mary always was, honest and completely authentic," he said. "That's the way she sang, too, honestly and with complete authenticity," Yarrow told The Associated Press.
Travers underwent a successful bone marrow transplant to treat her leukemia and while she could perform after that, she told WTOP radio in Washington that her condition had worsened earlier this year.
Noel "Paul" Stookey praised Travers for her inspiring activism, "especially in her defense of the defenseless."
"I am deadened and heartsick beyond words to consider a life without Mary Travers," he told The Associated Press.
The band's publicist, Heather Lylis, said Travers died at Danbury Hospital in Connecticut.
Mary Allin Travers was born Nov. 9, 1936, in Louisville, Ky., to two journalists who moved the family to New York's Greenwich Village. She attended school through the 11th grade before pursuing a singing career.
Pete Seeger, a founding member of the folk group the Weavers, lived in the same building as the Travers family and Travers performed with him.
Travers backed Seeger on one album and for two shows at Carnegie Hall, but it wasn't until she connected with Yarrow and Stookey that she found worldwide success. Yarrow was managed by Albert Grossman, who later worked with Bob Dylan.
The trio rehearsed in Travers' apartment for several months before its 1961 debut at the Bitter End in New York City.
The group won five Grammy Awards for its three-part harmony for "Leaving on a Jet Plane," "Puff the Magic Dragon" and Bob Dylan's "Blowin' in the Wind."
Travers is survived by her fourth husband, Ethan Robbins, and daughters Alicia and Erika.
The Associated Press contributed to this report.