
The six-time all-star and the team have yet to agree on treatment, which could include either surgery or rest in a cast. Either option is expected to take more than four months.
Houston had won 12 straight games heading into Tuesday night's game against the Washington Wizards. The Rockets are 36-20, three games behind the Los Angeles Lakers for the best record in the Western Conference.
Morey called it "a difficult day" for the Rockets and their fans.
"We've been playing exceptional ball," he said. "Yao's been a huge part of that."
Houston team physician Tom Clanton said that Yao has a chance to recover in time to play for China in the Beijing Olympics, which begin on August 8.