Nevada attorney general Adam Laxalt filed the lawsuit in Texas on Tuesday, urging the court to block implementation before the regulation takes effect in December.
The measure would shrink the so-called "white collar exemption" and more than double the salary threshold under which employers must pay overtime to their workers.
Laxalt said the rule would burden private and public sectors and represents inappropriate federal overreach.
Officials from the Labor Department didn't immediately respond to requests for comment.
Other plaintiffs include Alabama, Arizona, Arkansas, Georgia, Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Michigan, Mississippi, Nebraska, New Mexico, Ohio, Oklahoma, South Carolina, Texas, Utah and Wisconsin.