The location of the cemetery is unknown and the grave was marked by a wooden cross and a number known only to the deceased's family, Italian daily La Repubblica reported.
Priebke was 100 when he died in October while living under house arrest in Rome for the reprisal killing of 335 Italian men and boys in 1944.
The former SS officer's body was taken to Pratica di Mare airport, an Italian Air Force installation, after a funeral performed near Rome by an ultra-traditionalist breakaway Catholic group was sent into chaos by clashes between protesters and neo-Nazis.
Since then Italy has been trying to locate a proper burial site for Priebke because neither Germany nor other countries with a claim would accept the body and Italian officials feared his tomb would become a shrine for neo-Nazis, ANSA said.
La Repubblica said burial took place on a Sunday at the end of October and that the number on the grave would be released to Priebke's son in December.