It would be among the most restrictive abortion measures in the country. Critics of the bill claim many women do not know they are pregnant at the six-week mark.
The bill's sponsor, State Sen. Kristina Roegner, said using the existence of a fetal heartbeat as the defining line is clearer than determining the fate of a fetus based on its growth outside the womb, a marker established in court precedent. Roegner said viability can vary depending on the technology available and the medical care.
"[Viability] is a moving target, and we need a new standard," she said. "The heartbeat bill provides a sensible solution."
Similar measures approved by lawmakers were vetoed twice before by DeWine's predecessor, Republican John Kasich. He said such a law would create a costly court battle and likely be found unconstitutional.
In its current form, the bill includes an exemption if a mother’s life is at risk. Critics say it provides no exemptions for victims of rape or incest.
The legislation's passage in the Senate continued a celebratory week for abortion opponents in Ohio, where a divided federal appeals court upheld a state law Tuesday that blocked public money for Planned Parenthood
A handful of other states are considering legislation to restrict abortions once a fetal heartbeat can be detected.
The Associated Press contributed to this report.