Gordon suffered the injury in a loss to the Sacramento Kings On Thursday evening, the 14th consecutive franchise this season. It averages 17.8 points for the Rockets, who fell to 11-24 and 14 in the Western Conference.
Gordon, 32, had been targeted by multiple teams before the March 25 close of trading, but the injury largely ensures that he will end his fifth season in Houston.
The missiles parted with forward P. J. Tucker on Thursday evening until a deal can be found and had guards John Wall and Victor Oladipo in and out of the lineup with injuries. Launch center Christian Wood is expected to return to the lineup in the near future.