The Michigan measure, called Proposal 2, was backed by Ward Connerly, the former University of California regent who also backed California's law, Proposition 209, approved in 1996.
Unofficial final election results today said 58.1 percent voted "yes" on Proposal 2, with 41.9 percent against.
University of Michigan President Mary Sue Coleman said she would investigate an immediate legal challenge to the proposal, which officials said would severely hamper efforts to ensure a diverse student body.
"I will not allow this university to go down the path of mediocrity. I will not stand by and let the very heart and soul of this university be threatened," Coleman said in a speech to the campus. "Diversity makes us strong, and it's critical to our mission, it's critical to our excellence -- too critical to simply abandon."
A spokesman for the group backing Proposal 2 said he expected loud complaints by affirmative action backers but said he also hoped they would honor the public's decision.
"The people who support race preferences are going to stomp their feet, beat their chests and say this isn't fair," said Doug Tietz, a spokesman for the Michigan Civil Rights Initiative. "We need to make sure that people are obeying the law."
Connerly's Sacramento-based group, the American Civil Rights Coalition, was a major financial backer of the proposal.