Shams Charania of Stadium and The Athletic reported the update on Green's foot fracture Tuesday.
Green broke his left foot during a preseason game against the Toronto Raptors on Thursday, per ESPN's Tim MacMahon.
The 33-year-old Houston native averaged 9.2 points and 2.5 assists while shooting 35.4 percent from three-point range across 73 appearances off the bench for the Rockets last season.
He was likely to once again serve as the second wing player off the bench behind Eric Gordon this season.
Rockets head coach Mike D'Antoni told reporters Monday that Austin Rivers, Ben McLemore, Thabo Sefolosha and Chris Clemons could all see more playing time in Green's absence.
Houston has two preseason games left this week against the San Antonio Spurs and Miami Heat. The Rockets open the regular season Oct. 24 when they take on the Milwaukee Bucks.
Green is scheduled to become an unrestricted free agent after the 2019-20 campaign.