Her husband, Thomas FitzGerald, says she died Tuesday at their home in Southwick, Mass. The cause was cancer.
Nielsen was the only doctor at the Amundsen-Scott South Pole Station when she found a lump in her breast in June 1999, raising fears of cancer. Weather conditions didn't permit a rescue, so she performed a biopsy on herself with the help of staff.
She began treating herself using drugs dropped by parachute in the dark polar winter in July, in a mission documented by CBS News.
Despite her illness Nielsen kept busy with her duties up until she left the South Pole, her sister-in-law, Diana Cahill, told CBS News in 1999.
"She didn't have time to focus on her condition at all. She's a very giving person," Cahill said.
Following the dramatic airlift, she told The Vindictor newspaper she wanted to return to the Antarctic.
"It was such a wonderful place. I still love it. I would do it again. Even knowing what happened to me, it was the best year of my life," Nielsen told the newspaper.
Her cancer went into remission until 2005.