The lawsuit, filed in U.S. District Court in San Diego, claims that the new rule violates the Civil Rights Act and disproportionately affects minority coaches.
The action came after Dominic Hardie, who had coached high school girls' basketball teams in NCAA tournaments in the past, was unable to renew his certification because of a nonviolent drug conviction more than a decade ago.
Hardie is seeking a preliminary injunction to allow him to coach in an upcoming game in San Diego. His legal team, which includes the Lawyers' Committee for Civil Rights Under Law, said the new policy has a chilling effect on minority coaches.
The NCAA previously allowed people with a nonviolent felony conviction older than seven years to coach at NCAA-certified basketball tournaments. In 2011, the rule changed and all ex-felons were prohibited from coaching.
In a statement, the NCAA said it stands by its policy.
"Our policy has been unsuccessfully challenged in court previously. We continue to believe convicted felons should not have access to youth at events where NCAA coaches are participating, and we will vigorously defend this lawsuit," Bob Williams, NCAA vice president of communications, said in a statement.