Green will seek more options on his foot this week, reports Charania. There's no definite timetable for his return.
He was initially diagnosed with a sprained left foot and didn't practice Sunday.
Green posted five points and four boards in Houston's most recent preseason game in Japan against the Toronto Raptors.
The 33-year-old was a key reserve for the Rockets last season, averaging 9.2 points and shooting 35.4% from beyond the arc. Green's prolonged absence is a big blow to a Houston squad already lacking options on the wing.
Journeyman guard Ben McLemore is one of the candidates to fill in for Green. The former seventh overall pick shot 41.5% from distance during a brief 19-game stint with the Sacramento Kings last season.
Danuel House is another alternative for the Rockets after connecting at a 41.6% clip on 4.6 triples attempted per game during the previous campaign.