Their lawsuit was filed in Macomb County Circuit Court on Monday, according to their lawyer James Makowski.
The ordinance bans keeping an unsecured firearm in an unlocked vehicle.
A first offense is a civil infraction subject to a fine up to $350. A second or further offense is a misdemeanor punishable by a fine up to $500 or up to 90 days in jail or both.
The lawsuit asks the judge to throw out the ordinance.
Makowski said the plaintiffs are not trying to promote irresponsible gun ownership.
"The whole crux of the lawsuit is that Eastpointe lacks the authority to do what they're doing," said Makowski.
Makowski said that's because state law preempts a local unit of government from regulating the transportation or possession of firearms.
"If the legislature wants to address it, that is completely up to the legislature," said Makowski. "But Eastpointe lacks the authority, and by passing this ordinance, they are usurping state authority."
At a hearing on October 1 to consider the ordinance, the City's Public Safety Director George Rouhib said the police had received close to a dozen reports, in the preceding thirty days, of firearms stolen from unlocked vehicles.
The City of Eastpointe could not be reached for comment about the lawsuit.