Harden, who is a left-handed shooter, injured the thumb in Saturday's loss to the Grizzlies. Jeremy Lin will most likely start in his place.
The 24-year-old guard is averaging 23.7 points per game this season and is shooting 44 percent from the field.
The Rockets, who are 4-2 without Harden this season, have beaten the Spurs the two times they've met this season. Harden scored 31 points in the first game and 28 in the second.
Harden will likely be a game-time decision on Wednesday in Dallas, according to Jonathan Feigen of the Houston Chronicle.
James Harden is out tonight with a bruised left thumb sustained Saturday night against the Grizzlies.
— Jason Friedman (@JasonCFriedman) January 28, 2014
Harden will likely be a game-time decision tomorrow in Dallas. He is making the trip with the team after tonight's game. — Jonathan Feigen (@Jonathan_Feigen) January 28, 2014