Harden suffered the injury during Sunday's 148-142 double-overtime win over the Los Angeles Lakers.
Harden finished the victory with 40 points and 11 assists, helping Houston snap a five-game losing streak.
The five-time All-Star is enjoying an MVP-caliber season by averaging a league-leading 32.3 points per game to go along with 9.1 assists, 5.0 rebounds and 1.8 steals.
Houston is second in the Western Conference with a 26-9 record, and it entered play Monday trailing the Golden State Warriors by two games for the No. 1 seed.
Harden has been one of the NBA's biggest iron men in recent years, missing only two games from 2014-15 through 2016-17.
He has yet to miss a contest this season, but the Rockets will be forced to play at least six or seven games without him based on the timeline for his re-evaluation.
While Harden is on the shelf, the Rockets may be compelled to thrust reigning NBA Sixth Man of the Year Eric Gordon into a starting role, although he is already averaging 32.5 minutes per game.
There will also be a greater offensive burden on point guard Chris Paul, and the likes of Bobby Brown and the recently acquired Gerald Green should see more consistent playing time as well.