Ride died at her home in the San Diego suburb of La Jolla, said Terry McEntee, a spokeswoman for her company, Sally Ride Science.
She was a private person and the details of her illness were kept to just a few people, she said. Ride rode into space on the shuttle Challenger in 1983 when she was 32.
After her flight, more than 42 other American women flew in space, Nasa said. "Sally was a national hero and a powerful role model. She inspired generations of young girls to reach for the stars," president Barack Obama said.
"People around the world still recognise her name as the first American woman in space, and she took that title seriously even after departing Nasa," Eileen Collins, the first female space shuttle commander, said. "She never sought media attention for herself, but rather focused on doing her normally outstanding job."
When Ride first launched into space, feminist icons such as Gloria Steinem and Jane Fonda were at Kennedy Space Centre and many wore T-shirts alluding to the pop song with the refrain of the same name: "Ride, Sally Ride."
Nasa administrator Charles Bolden, a former astronaut, said Ride "broke barriers with grace and professionalism - and literally changed the face of America's space programme".
He added: "The nation has lost one of its finest leaders, teachers and explorers." Ride was a physicist, writer of five science books for children and president of her own company.
She had also been a professor of physics at the University of California in San Diego. She was selected as an astronaut candidate in 1978, beating out five women to be the first American female in space.
Her first flight came two decades after the Soviets sent a woman into space. "On launch day, there was so much excitement and so much happening around us in crew quarters, even on the way to the launch pad," Ride recalled in a Nasa interview for the 25th anniversary of her flight in 2008.
"I didn't really think about it that much at the time - but I came to appreciate what an honour it was to be selected to be the first to get a chance to go into space."
Ride flew in space twice, both times on Challenger in 1983 and in 1984, logging 343 hours in space. A third flight was cancelled when Challenger exploded in 1986.
She was on the commission investigating that accident and later served on the panel for the 2003 Columbia shuttle accident, the only person on both boards. She also was on the president's committee of science advisers.
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