Harden was sidelined with a sore foot, the team tweeted.
Harden has averaged 24.9 points, 5.1 assists and 4.6 rebounds per game this season for a Rockets team that was playing the first game of a road back-to-back.
Carter-Williams, who was named the league's player of the week the first week of the season, is day to day with a left foot arch bruise, according to the Sixers' official Twitter feed.
The Sixers rookie has averaged 17.4 points, 7.6 assists, 5.4 rebounds and 2.6 steals per game for a Philadelphia team that has gotten off to a surprising 4-4 start.
Tony Wroten notched a triple-double with 18 points, 10 rebounds and 11 assists while starting in Carter-Williams' place during the 123-117 overtime victory. Terrence Jones got the start for Houston and contributed 10 points, 11 rebounds and three blocks in the loss.