Navratilova said Melbourne's Margaret Court Arena should be renamed after another Australian great, Evonne Goolagong Cawley, after Court's comments caused a furore in the tennis community.
Court, 74, had already been criticised after she said she would avoid using Australian airline Qantas over its support for same-sex marriage, even before her latest salvo over Christian radio.
"Linking LGBT to Nazis, communists, the devil? This is not OK," Navratilova, who is gay, wrote in an open letter addressed to Margaret Court Arena and published by Australia's Fairfax newspapers.
"This is in fact sick and it is dangerous. Kids will suffer more because of this continuous bashing and stigmatising of our LGBT community."
Navratilova added: "It is now clear exactly who Court is: an amazing tennis player, and a racist and a homophobe.
"The platform people like Margaret Court use needs to be made smaller, not bigger.
"Which is why I think it's time to change your name. And I think the Evonne Goolagong Arena has a great ring to it.
"Now there is a person we can all celebrate."
By calling Court "racist", Navratilova was referring to her 1970 comments about apartheid, when she said: "South Africans have this thing better organised than any other country."
Hitler and communism
On Wednesday, Court, who is a church pastor, told Vision Christian Radio that she wasn't "against" gay people but wanted to "help them overcome".
She also claimed that transgender children had had their minds corrupted, comparing the phenomenon to brain-washing by Hitler and communist countries.
"That's all the devil... but that's what Hitler did and that's what communism did – got the mind of the children," said Court.
"And there's a whole plot in our nation, and in the nations of the world to get the minds of the children."
Court's comments sparked disbelief among current players with Australia's Sam Stosur describing them as "crazy".
Some have called for her name to be stripped from Melbourne's Margaret Court Arena, and there have even been rumblings of a boycott of the stadium at next year's Australian Open.
Stosur's fellow Australian Casey Dellacqua has also criticised Court, whose record of 24 major titles still stands, for her "hurtful" views on same-sex relationships.
Dellacqua, who has two children with her partner Amanda Judd, said Court was wrong to claim that her children "have been deprived of a father" and that such youngsters are not "given the best possible start in life".
Navratilova said she had "long ago forgiven" Court for her comments 27 years ago that being a lesbian made her a bad role model.
But "demonising" and denying LGBT people rights was unacceptable, the nine-time Wimbledon champion said.
"Too many will die by suicide because of this kind of intolerance, this kind of bashing and yes, this kind of bullying. This is not OK," she added.