Payton, who returned to the starting lineup Friday after missing nine games with a right ankle sprain, suffered the injury about eight minutes into the first quarter and did not return.
He will visit a hand surgeon next week, after which a timetable for his return will be known.
"Since I've been here, it's always something," said Anthony Davis, who had 43 points against the Knicks. "He just got back off an injury. You know, he was eager to get back, and then this happens. Hopefully it doesn't sideline him for too long, and I hope he gets healthy soon. We know he wants to be here and be on the floor for us, but try to just get it right, and we've got guys who can step up and take his place, like we did the past couple of games he was out."
Wesley Johnson started the second half in Payton's place.
Acquired as a free agent this past offseason, Payton, 24, entered the day averaging 11.6 points and 6.4 assists in five games this season.
New Orleans has won four of its past five games.
The Associated Press contributed to this report.