Gordon suffered the injury in a loss to the Sacramento Kings on Thursday night, the franchise's 14th consecutive this season. He's averaging 17.8 points for the Rockets, who dropped to 11-24 and 14th in the Western Conference.
Gordon, 32, had been a target of several teams ahead of the March 25 trade deadline, but the injury largely assures that he will finish his fifth season in Houston.
The Rockets separated with forward P.J. Tucker on Thursday night until a trade can be found and have had guards John Wall and Victor Oladipo in and out of the lineup with injuries. Starting center Christian Wood has been out since early February with an ankle injury.
First-year coach Stephen Silas is optimistic Wall, Wood and Danuel House (knee) could be back by Tuesday.