Clarke played only three minutes in Memphis' loss to the LA Clippers on Monday, due to what the team initially called right hip soreness.
According to the Grizzlies, additional testing revealed that Clarke suffered a quad injury, with the team saying he will be reevaluated in two weeks.
Memphis already is without Jaren Jackson Jr., who is expected to miss at least two weeks because of a left knee sprain. Clarke started in Jackson's place on Monday.
Clarke, the rookie first-round pick out of Gonzaga, is averaging 12.0 points and 5.8 rebounds this season while shooting 62.3% from the field.