This guide from the Michigan Farmers Market Association lists markets by region and county.
This listing of Michigan farmers markets from Farmers Markets Online lists markets by town.
The Ann Arbor Farmers Market is open Wednesdays and Saturdays (7 a.m. to 3 p.m.) May through December and Saturdays only (8 a.m. to 3 p.m.) January through April. You'll find the market at 315 Detroit Street, Ann Arbor.
Detroit's Eastern Market is packed with vendors selling local goods from Michigan, Ohio, and near parts of Canada, but also retail vendors with goods form around the world. It's open Monday through Saturday from 7 a.m. to 5 p.m., with fresh farm vendors coming in the greatest number on Saturdays.
Sweetwater Local Foods Market sells only locally grown produce and animal products raised in a manner that enhances biological diversity, builds soil health, and respects animal welfare. It's open at Hackley Health at the Lakes in Muskegon in Western Michigan every Saturday, 9 - 1 from late spring until Christmas time and every other Saturday from early January until spring.