Per Shams Charania of The Athletic and Stadium, Green is believed to have broken his left foot and could miss "a few months" pending additional medical opinions.
The injury occurred during Houston's 118-111 preseason win over the Toronto Raptors on Thursday. He sat out Sunday's practice with what the team called a sprained foot, per Jonathan Feigen of the Houston Chronicle.
ESPN's Tim MacMahon noted the Rockets hope Green will be able to avoid having surgery.
Green, 33, is entering his third consecutive season with Houston. The veteran forward signed a one-year deal in July to remain with the club. He averaged 9.2 points per game and shot 35.4 percent from three-point range in 73 appearances last season.
If Green is forced to miss time during the regular season, Rockets head coach Mike D'Antoni has Ben McLemore to use in the swingman role.
Houston opens the 2019-20 season on Oct. 24 against the Milwaukee Bucks.