The so-called "baby-bonus" of €2,000 (£1,420) has been designed to encourage couples to have more babies.
The financial incentive comes as concerns grow over the country's low birth rate.
Claimants must be Italian and committed Catholics who were married in the church, while the pay-out only becomes available when a couple give birth to their third child.
Fr Stefano Bimbi, said in The Daily Telegraph, he was keen to help people that were concerned about the cost of a big family.
So far four couples in Staggia Senese, a town near Siena, have received the funds.
