House Bill 252 would force the woman to provide a list of possible fathers and make it illegal for doctors to perform abortions without the father's consent.
Ohio would be the first state in the nation to pass a law like this.
"What does the father have to say in the abortion of his child? He has nothing to say," said State Rep. John Adams, in defense of the bill.
Pro-choice Ohio issued a statement saying Adams' bill is "completely out of touch with Ohio's mainstream values. The measure is a clear attack on a woman's freedom and privacy."