Anatoly Belonog said the diagnosis had already been confirmed and that nine other suspected carriers were undergoing additional tests.
"The cause of the contamination is a gross violation of sanitary norms at medical institutions," he said, adding that the virus must have been transmitted through transfusions of blood or its components or through poorly sterilized medical instruments.
Ualikhan Akhmetov, the head of the Health Ministry's medical services quality control committee, said: "The HIV-positive children have been repeatedly admitted to hospitals in the city of Shymkent [an administrative center in southern Kazakhstan], where they received intramuscular and intravenous injections."
Health Minister Yerbolat Dosayev pledged to provide the full range of antiretroviral treatment for the infected children.
Ministry statistics show that 828 people in Kazakhstan tested positive for HIV in January-June 2006 and 70 new AIDS cases were detected - almost double the figure for the same period last year.
According to the World Health Organization, HIV is mainly spread in Kazakhstan by intravenous drug users sharing dirty needles.
The UN Office on Drugs and Crime puts the total number of HIV cases in Kazakhstan at 5,440.