Martin was hospitalized Wednesday and died Sunday, her husband, Ronald, told People.com.
Jolie, the 37-year-old mother of six young children, recently revealed she had a preventative double mastectomy after learning she had tested positive for the BRCA gene, which predisposes her to breast and ovarian cancers.
The actress' mother, Marcheline Bertrand, died of ovarian cancer in 2007 at the age of 56.
People.com said Jolie was not with her aunt when she died, but she had seen her many times since her diagnosis and had been in frequent contact this past week to lend her support.
"Angelina has been sending her wishes," Ron Martin told People.com. "She and my wife texted each other. It was difficult for my wife, during the last few months, to communicate."
Jolie's uncle called the film star's decision to have a preventive double mastectomy "the smartest thing on earth."
"It takes a lot of courage to have your breasts removed," he said.