That brings the total who have tested positive for hepatitis to 33.
They are among thousands tested because they were treated with endoscopic equipment that wasn't properly sterilized between patients and exposed them to the body fluids of others. The equipment is often used in colonoscopies and ear, nose and throat procedures.
Nearly 11,000 former sailors, soldiers, airmen and Marines could have been exposed at the hospitals in Miami, Murfreesboro, Tenn., and Augusta, Ga. The agency said 6,687 patients have been notified of their test results so far.
VA spokeswoman Katie Roberts said the new HIV case was found in the Miami hospital. The agency said in a news release the positive tests were "not necessarily linked to any endoscopy issues."
"It's very disturbing that anybody would contract it, of course. I am pleased that the VA has agreed to treat all the veterans regardless of where they may have contracted it," said Alexander Kovac, a veterans' advocate who was stationed in Korea in the 1960s.
The VA has said the problems with the endoscopic equipment had gone on for years, but were discovered in December when officials learned the Murfreesboro facility wasn't following cleaning procedures the manufacturer recommended. It issued an internal alert for hospitals to check procedures, and the problem at Augusta was discovered in January.
On Feb. 9, the VA announced a nationwide safety check of endoscopic equipment used in colonoscopies and ear, nose and throat treatments. The procedure involves a narrow, flexible tube fitted with a fiber-optic device such as a telescope or magnifying lens that is inserted into the body.
Some veterans were warned in February to get tested, and more were alerted in March when the Miami hospital backtracked on its previous conclusion that it didn't have a problem.