The injury occurred on Sunday night in the Rockets' game against the Lakers.
The team said doctors would re-evaluate Harden's injury in two weeks. Houston went 0-3 while guard Chris Paul recovered from a strained left adductor.
Harden has been one of the NBA's biggest iron men in recent years, missing only two games from 2014-15 through 2016-17.
Houston (26-9) have lost five of their last six games to fall to second in the Western Conference.
Harden, who also ranks third in the league with 9.1 assists per game, has been durable throughout his career.
The five-time All-Star had only missed two regular-season games over the previous three seasons combined and has played in all 35 games this season. Beyond just this being a major purchase for Paul and his family, it will immediately lead to the assumption that he could be thinking about remaining with the Rockets long-term past this season. Since I have been here, he's been here, he has been on the court, he has been available.