The severity of Kidd's injury is unclear, but he did not travel with the team to the Barclays Center.
"I don't know much yet," Knicks coach Mike Woodson said after the game. "He's back home and we'll evaluate him tomorrow, and we'll go from there."
Ronnie Brewer started in Kidd's place at shooting guard but left in the second half with a dislocated left fourth finger. X-rays were negative.
Heading into the postgame locker room, Brewer told ESPN, "I'm fine."
Kidd, 39, had played in the Knicks' first 12 games and established himself as a vital piece for New York.
An 18-year-veteran, Kidd had started at shooting guard for the Knicks in their first 12 contests, averaging 8.0 points, 2.1 steals, 3.4 assists and 3.3 rebounds in 26 minutes per game.
Kidd also has been a calming influence on New York's backcourt; the Knicks entered Monday's contest averaging an NBA-low 11.2 turnovers per game while leading the league in offensive efficiency, which is a measure of points scored per 100 possessions.
"He's a big part of what we do," Woodson said following the loss. "He's one of those veteran guys that can settle things down and help run the team if things are not going great and smoothly."
Ian Begley is a regular contributor to ESPNNewYork.com. Information from ESPNNewYork.com contributor Jared Zwerling was used in this report.