Davoud Kazemi, who is in charge of the contest, told Reuters that each of the 12 winners would have their cartoons published and receive two gold coins (worth about $140 each) as a prize.
Protesters hurled petrol bombs and stones at the Danish Embassy in Tehran for a second successive day on Tuesday.
Iranian regime announced it had cut all trade ties with Denmark because of the cartoons and hundreds of protesters hurled rocks and fire bombs at the Danish embassy on Monday night.