The cure was announced by Gero Hutter and Eckhard Thiel, blood cancer specialists at Charite Hospital in Berlin.
While the case has novel medical implications, experts say it will be of little immediate use in treating AIDS.
The patient, a 42-year-old American resident in Germany, also has leukemia, which justified the high risk of a stem-cell transplant.
Such transplants require wiping out a patient's immune system, including bone marrow, with radiation and drugs; 10 to 30 percent of those getting them die.
"Frankly, I'd rather take the medicine," said Robert Gallo, director of the Institute of Human Virology at the University of Maryland School of Medicine, referring to antiretroviral drugs.
Attempts to use bone-marrow transplants in AIDS treatment have been made since the 1980s.
In one case, a patient with both AIDS and lymphoma died of the cancer two months later, but was found to harbor no HIV; it was not known if something in the transplant had protected him.
And in a famous 1995 case, Jeff Getty, a prominent San Francisco advocate for AIDS patients, received bone marrow from a baboon, which is resistant to the human virus.
He survived 11 years, but died of AIDS and cancer; the transplant had not protected him but antiretroviral triple therapy had been invented in time to help.
Hutter said one of the 80 potential donors who matched his patient closely enough for leukemia treatment also happened to have the mutation.
Even if it is prevented from replicating by drugs, the HIV can lie dormant in lymph and nerve cells for years.
But without the necessary receptors, any virus coming out of dormancy has no way to infect them.
Doctors say the case gives hope for therapies that artificially induce the Delta 32 mutation.
For example, Irvin S. Y. Chen, director of the AIDS Institute at UCLA, is working on using RNA "hairpin scissors" to cut out the bits of genetic material in blood stem cells that code for the receptors.
The concept is working in monkeys, he said. Eventually, he hopes, it will be possible to inject them into humans after wiping out only part of the immune system with drugs.