O Globo newspaper said the positive result of the AIDS exam was confirmed by the Brazilian Bishops Conference.
The bishops said that the priest apparently contracted the disease before his ordination in 1990.
He is confined to a psychiatric ward of a detention centre, since the doctors who saw him diagnosed him as suffering from 'mental disturbances'.
Dantas Rolim was suspended from his duties as a parish priest in the city of Petropolis six months ago due to his mental problems, the bishops conference said.