The case of a middle-aged woman of mixed race, presented at the Conference on Retroviruses and Opportunisitic Infections in Denver, is also the first involving umbilical cord blood, a newer approach that may make the treatment available to more people.
Since receiving the cord blood to treat her acute myeloid leukaemia - a cancer that starts in blood-forming cells in the bone marrow - the woman has been in remission and free of the virus for 14 months, without the need for potent HIV treatments known as antiretroviral therapy.
The two prior cases occurred in males - one white and one Latino - who had received adult stem cells, which are more frequently used in bone marrow transplants.
"This is now the third report of a cure in this setting, and the first in a woman living with HIV," Sharon Lewin, President-Elect of the International AIDS Society, said in a statement.
The case is part of a larger US-backed study led by Dr Yvonne Bryson of the University of California Los Angeles, and Dr Deborah Persaud of Johns Hopkins University in Baltimore.
It aims to follow 25 people with HIV who undergo a transplant with stem cells taken from umbilical cord blood for the treatment of cancer and other serious conditions.
Patients in the trial first undergo chemotherapy to kill off the cancerous immune cells. Doctors then transplant stem cells from individuals with a specific genetic mutation in which they lack receptors used by the virus to infect cells.
Scientists believe these individuals then develop an immune system resistant to HIV.
Lewin said bone marrow transplants were not a viable strategy to cure most people living with HIV. But the report "confirms that a cure for HIV is possible and further strengthens using gene therapy as a viable strategy for an HIV cure", she said.