The strike is the first against GM over a local contract agreement since a lengthy walkout in Flint back in 1998, said GM spokesman Dan Flores.
United Auto Workers members walked off the job just after a deadline passed at 10 a.m.
The factory, which employs about 3,400 hourly workers, makes the Buick Enclave, Saturn Outlook and GMC Acadia crossover vehicles that are selling well for GM.
UAW Local 602 official Harold Brown handed out "UAW On Strike" signs from the trunk of his car as workers left the plant. He reminded them to go to the union hall to leave telephone numbers and sign up for picket duty.
Tim Berry, 50, of Holt, said the strike was justified.
"Since we've been out here, we haven't really had a local agreement," the 32-year GM quality control worker said of the Delta Township plant. "We should be able to have an agreement."
Local plants negotiate their own operating agreements separate from the national contract, which was settled last year. The local contract deals with issues such as overtime and work rules.
Flores said the company was disappointed workers left their jobs.
"We remain focused on reaching an agreement as soon as possible," he said.
Industry analysts have speculated that the strike is an effort by the union to get GM involved in a two-month walkout at parts supplier American Axle and Manufacturing Holdings Inc.
Flores would not comment when asked about a possible American Axle connection and said he did not know the specific issues involved in the Delta Township walkout.
The UAW has been on strike against American Axle for nearly two months, and more than 30 GM plants have been affected by that strike.
So far, the strike has mainly affected production of GM's trucks and sport utility vehicles, which were selling slowly anyway. But a strike against the Delta Township plant could have a more serious impact. GM has only a 40-day inventory of the Buick Enclave, compared to an inventory of more than 150 days on some large trucks and SUVs when the American Axle strike began, according to Ward's AutoInfoBank. A 60-day supply is considered ideal in the industry.
In addition to Delta Township, workers at metal fabricating plant near Grand Rapids and a transmission plant in Warren, Mich., also have threatened to strike.
Local unions in Arlington, Texas; Parma, Ohio; and Flint also had threatened strikes but since have withdrawn those threats.