The bill targets about $1.3 million in funding Planned Parenthood gets through Ohio's health department. Most of that money goes to HIV testing, breast and cervical cancer screenings and preventing violence against women.
The legislation, which doesn't specifically name Planned Parenthood, takes the funding from groups that carry out or promote abortions.
The Republican presidential candidate was expected to sign the measure, despite opposition from some Democrats, though he did not do so in public.
Many Republican presidential candidates have said they plan to defund Planned Parenthood if they get the nomination.