The ad, which appeared in both Sainsburys and Delicious magazines, showed the nun wearing a full habit and the priest sporting rosary beads and holding a pot of ice cream. Text stated: "Kiss temptation."
Ten people complained that the ad was offensive to people who have chosen to pursue religious vocations where celibacy is integral to their calling.
The advertiser said the ad was intended as a tongue-in-cheek portrayal of forbidden Italian temptations, which the ice cream represented.
The ASA noted the ad played on the theme of forbidden temptations without actually showing the pair kissing.
However, the watchdog considered that the ad showed the priest and nun in a sexualised manner and the implication that they were hovering on the brink of temptation could cause offence to some readers.
The ad must not appear again in its current form.