The Canadian-born actress died at her home in the US state of Montana on Sunday.
Her cause of death was not confirmed by the Franzen-Davis funeral home.
Kidder starred opposite leading man Christopher Reeve in the 1978 film Superman and went on to appear in its three sequels.
She maintained a close relationship with Reeve until his death in 2004, telling the US news channel CBS: “When you’re strapped to someone hanging from the ceiling for months and months, you get pretty darned close.”
Kidder publicly criticised a decision for Richard Donner to be replaced as director for Superman II in 1980.
This was later reported as the reason she appeared in less than five minutes of Superman III four years later.
She returned in 1987 for the much-maligned Superman IV: The Quest for Peace.
Kidder re-entered the Superman story in 2004 when she appeared as Dr Bridgette Crosby in Smallville, a TV drama about a young Clark Kent coming to grips with his powers.
Star Wars actor Mark Hamill paid tribute to her, writing on Twitter: “On-screen she was magic. Off-screen she was one of the kindest, sweetest, most caring woman I’ve ever known.
“I’ll miss you #MargoKidder. Your legacy will live on forever.”
In the early years of her career she appeared in the 1975 movie The Great Waldo Pepper and the children’s TV series R L Stine’s The Haunting Hour in 2014.
The actress, who leaves behind a daughter, was married and divorced three times in her life.
Kidder said after her third marriage ended in 1984 that she prefers the companionship of her dogs.
Her first husband was the American novelist Thomas McGuane with whom she had her daughter Maggie McGuane in 1976.
She later wed the US actor John Heard in a marriage that lasted just six days.
Kidder was married to film director Philippe de Broca from 1983 to 1984.
She also dated former Canadian prime minister Pierre Trudeau, the film director Steven Spielberg, and the comedian Richard Pryor.
The actress suffered a mental health breakdown in the 1990s and disappeared for four days in a highly publicised episode.
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She was later diagnosed with bipolar disorder.
Acting work dried up for several years, but Kidder later re-emerged with a guest starring role in TV shows including the L Word, a drama about a group of lesbians and bisexuals living in Los Angeles.