The Hollywood entertainment website E! News cited Jolie's uncle, Ron Martin, as saying that his wife, Debbie – the younger sister of Jolie's late mother – died early on Sunday at Palomar Hospital in Escondido, California.
"Angelina has been in touch throughout the week and her brother Jamie has been with us, giving his support day by day," Martin was quoted as saying on E!'s website.
"They both loved Debbie very much and although Angie is not able to come right now she has sent her love and support which was very nice."
Jolie (37) revealed in an article in the May 14 edition of the New York Times that she chose to undergo surgery to minimise the risk she might develop breast cancer due to the inheritance of a "faulty gene".
The actress's partner and fellow screen star Brad Pitt led worldwide praise, declaring Jolie heroic, followed by her doctors, other stars and thousands of supporters, who took to social media to praise her openness.
Jolie and Pitt have six children – three adopted and three biological.
Dangerous gene
The actress's mother, Marcheline Bertrand, died of ovarian cancer at the age of 56 and passed on the gene, BRCA1, that put Jolie at higher risk.
Jolie's doctors estimated she had an 87% risk of developing breast cancer and a 50% risk of ovarian cancer, prompting her to take action to cut the chances that she might die at a young age.
The actress said in the newspaper article that her likelihood of developing breast cancer is now just 5%, though she still runs a relatively high risk of contracting ovarian cancer.
Jolie, respected for her humanitarian work overseas with the United Nations, said she was speaking out to help other women understand their options and also to urge governments in lower-income countries to provide the health care women need.
"I started with the breasts, as my risk of breast cancer is higher than my risk of ovarian cancer, and the surgery is more complex," she wrote.
"I can tell my children they don't need to fear they will lose me to breast cancer."
Cancer campaigners cheered Jolie but warned women against rushing out to be tested for the gene mutation that threatened the actress's life.
Not only is the BRCA1 mutation rare in the female population, they said, but it is also expensive to test for – Jolie paid $3 000 at a US laboratory that controversially claims patent rights on the gene. – AFP