The museum's suing the folks behind a Las Vegas show called "Hitzville the Show: Motown Revue" ... claiming the name is too similar to its Detroit museum, Hitsville U.S.A. -- the iconic home of the Motown sound.

According to docs, the museum -- the original site of Berry Gordy's Motown record studio -- claims producers originally created the one-night show as a Hurricane Katrina fundraiser.

But, the museum's pissed producers brought the show to Vegas ... where the museum alleges producers have been cashing in on its name and the Motown sound for 6 nights a week.

Motown Museum -- which has owned the trademark for decades and licenses the "Hitsville" name to films and stage musicals -- says producers blew them off when they sent them a cease and desist letter in January, and the show continued.

It's now suing Jennifer Reeves and William Shack -- as well as their production company, Jabara Records, and the theater at which they perform -- demanding they drop the act and turn over profits producers have made while using the "Hitsville" name.