The Republican governor, who has said he opposes abortion, signed the contentious measure that passed the Michigan Legislature earlier this month.
The law requires facilities where at least 120 abortions are performed annually to obtain a state license as a freestanding outpatient surgical facility. The step would mean further inspections and higher costs for the clinics, in some cases requiring them to renovate their buildings.
Patients must undergo counseling with a health professional to make sure they aren't being forced to get an abortion. But a provision was dropped that would have established penalties for individuals trying to force a woman into getting a so-called "coercive" abortion.
Other provisions deal with disposal of fetal remains and require that a doctor perform a physical exam before prescribing drugs that would induce abortion. The exam could not be performed from a distance through use of a web-based camera, a process known as telemedicine, which critics said would impose a hardship on women in rural areas.
The measures were supported by Right to Life of Michigan and the Michigan Catholic Conference, which say they improve health and safety standards. They were renounced by Planned Parenthood of Mid and South Michigan, which countered the legislation imposes unreasonable requirements and threatens access to abortions.
Snyder said in a news release that the legislation "respects a woman's right to choose while helping her protect her health and safety."
Incoming House Democratic Leader Tim Greimel said in a statement that GOP leaders and Snyder "are ignoring a majority of Michiganders' belief that abortion should remain safe and legal in our state." He added that "Republicans should focus on the economy and job creation instead of extreme social policies that further divide our state."
The measure takes effect March 31.
Snyder also vetoed legislation he originally sought to end Blue Cross Blue Shield of Michigan's tax-exempt status and turn it into a customer-owned nonprofit. He objected to provisions added by lawmakers preventing insurers and businesses from providing elective abortion coverage in employee health plans.
The bills also would have excluded abortions for rape, incest or the health of the woman in the definition of elective abortion. That would have required women to buy separate, elective abortion coverage.
"I don't believe it is appropriate to tell a woman who becomes pregnant due to a rape that she needed to select elective insurance coverage," Snyder said. "And as a practical matter, I believe this type of policy is an overreach of government into the private market."
House Speaker Jase Bolger said in a statement that the Republican leadership "didn't seek to ban abortion coverage in any instances, including those mentioned in the governor's veto message."
Bolger said the future of Blue Cross' overhaul is "unclear," while Snyder and Blue Cross officials hope to get the bills approved in the upcoming legislative session.
"We are disappointed with the veto but understand the governor's decision," Blue Cross spokesman Andrew Hetzel said. "We also understand why he proposed the legislation in the first place."
The action by Snyder came on a busy day, as he dealt with more than 50 pieces of legislation. Lawmakers passed an estimated 282 bills in the so-called lame-duck session that brought the 96th Legislature to a close this month. Snyder spokeswoman Sara Wurfel said the governor has acted on 186 so far.