The bill allows health care workers to refuse service to anyone on moral, ethical or religious grounds.
The Republican dominated House passed the measure as dozens of Catholics looked on from the gallery. The Michigan Catholic Conference, which pushed for the bills, hosted a legislative day for Catholics on Wednesday at the state Capitol.
The bills now go the Senate, which also is controlled by Republicans.
The Conscientious Objector Policy Act would allow health care providers to assert their objection within 24 hours of when they receive notice of a patient or procedure with which they don't agree. However, it would prohibit emergency treatment to be refused.
Three other three bills that could affect LGBT health care were also passed by the House Wednesday which would exempt a health insurer or health facility from providing or covering a health care procedure that violated ethical, moral or religious principles reflected in their bylaws or mission statement.
Opponents of the bills said they're worried they would allow providers to refuse service for any reason. For example, they said an emergency medical technicians could refuse to answer a call from the residence of gay couple because they don't approve of homosexuality.
Rep. Chris Kolb (D-Ann Arbor) the first openly gay legislator in Michigan, pointed out that while the legislation prohibits racial discrimination by health care providers, it doesn't ban discrimination based on a person's sexual orientation.
"Are you telling me that a health care provider can deny me medical treatment because of my sexual orientation? I hope not," he said.
"I think it's a terrible slippery slope upon which we embark," said Rep. Jack Minore (D-Flint) before voting against the bill.
Paul A. Long, vice president for public policy for the Michigan Catholic Conference, said the bills promote the constitutional right to religious freedom.
"Individual and institutional health care providers can and should maintain their mission and their services without compromising faith-based teaching," he said in a written statement.