Richardson suffered the injury while lunging toward the ball in the first quarter of Wednesday's game against the Toronto Raptors. He exited the contest and did not return.
The 26-year-old has started all 38 of his appearances this season, averaging 15 points, 3.4 assists, and a steal per game.
Philadelphia was already without starting center Joel Embiid, who's missed the last eight contests due to a finger injury.
In 240 minutes with all five starters - Richardson, Embiid, Ben Simmons, Tobias Harris, and Al Horford - on the court together this season, the 76ers have posted a sparking 97.1 defensive rating while outscoring opponents by 8.3 points per 100 possessions.
After falling to Toronto on Wednesday, Philadelphia sits sixth in the Eastern Conference at 29-17.