The 33-year-old point guard played for 35 minutes in the 121-111 defeat to the Washington Wizards on Wednesday, scoring 24 points and adding 10 assists and five rebounds.
However, according to ESPN, he will miss a long stretch now, with the injury detected during the Wizards game and confirmed in tests on Thursday.
Harden joined Philadelphia in February from the Brooklyn Nets in a multi-player trade and this season he has averaged 22 points, 10 assists and seven rebounds through nine games.
The Sixers are 4-5 for the campaign so far.
Harden is a 10-time All-Star and was named MVP in the 2017-18 NBA season.
With Harden on board for the closing games of the 2021-22 campaign, the Sixers reached the Eastern Conference semi-finals in the playoffs, where they were beaten 4-2 in the best-of-seven series by the Miami Heat.