The measure was pushed as a "citizen-initiated" bill after Snyder vetoed similar legislation in 2012, so the measure cannot be vetoed or voted on in 2014 as a ballot measure.
Michigan joined twenty-three other states that have passed measures to keep women from using their private insurance to cover abortions.
The Planned Parent Action Fund on Wednesday called the trend "troubling."
"What's happening in Michigan is part of an outrageous and troubling trend. In just the last five months, politicians in Texas, North Carolina, Ohio, and Michigan have broken or bent the rules to jam through abortion restrictions that the public overwhelmingly opposes," Cecile Richards, president of PPAF, said in a statement.
"These extreme restrictions are so unpopular that politicians can’t pass them through the regular democratic process. Instead, they’re using every trick in the book — votes in the middle of the night, special sessions, and procedural loopholes — in order to pass these measures."