Two other anti-abortion bills were approved by the House. One would ban abortions after 20 weeks if a doctor has determined the fetus could survive outside the womb, and the other bars insurance companies that cover non-therapeutic abortions from participating in exchanges in Ohio under the Obama healthcare plan.
The Senate is expected to act on the abortion bills Wednesday.
Critics call the "Heartbeat Bill" the most stringent anti-abortion measure in the country.
"It prohibits abortions after only about six weeks, a time when many women do not yet even know they are pregnant," said Armond Budish, leader of the Democratic caucus in the House.
The state budget, which was approved Tuesday by the Senate, bars state hospitals from performing abortions. The House is expected to act on the budget bill Wednesday, and by law Gov. John Kasich must sign it by midnight Thursday.