Fr Giovanni Cavalcoli, a theologian known for his hardline views, made the comments on 30 October, the day central Italy was struck by a 6.6-magnitude quake - the most powerful to hit the country in 36 years.
It was the third major quake in the region in just over two months.
Cavalcoli told Radio Maria that the seismic shocks were “divine punishment” for “the offence to the family and the dignity of marriage, in particular through civil unions”.
Italy is one of the last western European countries to legally recognise same-sex relationships, having introduced legislation last month to allow gay civil unions.
The radio station distanced itself from Cavalcoli’s views and the Vatican has issued a stinging rebuke, saying the idea of a vengeful God was “a pagan vision” dating from “the pre-Christian era”.