Jonathan Feigen of the Houston Chronicle reported that Tucker has a "minor left ankle sprain" and will head back to Houston to recover.
Tucker, 34, averaged 7.3 points, 5.8 rebounds and 1.6 steals for the Rockets last season. The versatile 6'6" forward started all 82 regular-season games and 11 more in the playoffs.
"It's hard to have an injury in this situation," Tucker said. "USA Basketball is such a big deal, but then to have the NBA season coming up, it's tough. It's always hard for me because I want to play."
Tucker continued: "As bad as I want to play for USA, the Rockets, it's a big season for me. Selfishly I want to play for USA. It stinks. It's still fresh. So it still hurts."
He should be fine well in advance of the Rockets' regular-season opener Oct. 24 against the Milwaukee Bucks.
As for Team USA, two more cuts must be made to finalize a 12-man roster before heading to China for the World Cup.
The men's hoops national team may have bigger issues, however, as it just lost 36-17 to the following roster, per ESPN's Jonathan Givony:
Sam Amick of The Athletic reported that the squad beat Team USA by three points in another 10-minute scrimmage.
Five of the 11 members of the LA Select Team did not see any NBA court time last season. Washington Wizards guard Chasson Randle got the most run among his teammates, but he only averaged 15.2 minutes per game.
Team USA has time to recover in advance of the World Cup, as its first game isn't until Sept. 1 against the Czech Republic.
Until then, the Americans will train and play a few games against other countries, starting Friday against Spain in Anaheim, California.