The remarks, made on the station Radio Maria, were "offensive and scandalous", the Vatican said.
A Dominican friar said the quakes, including one in August that killed nearly 300, were caused by sins of man.
He said these included the approval of same-sex civil unions last May.
But the Vatican rejected the remarks as pagan, and said they had nothing to do with Catholic theology.
"They are offensive statements for believers and scandalous for those who do not believe", said Monsignor Angelo Becciu, deputy secretary of state, who is close to Pope Francis.