Felton was charged with second- and third-degree criminal possession of a firearm, which are felonies, and fourth-degree possession of a firearm, which is a misdemeanor, the spokesman said.
Felton is expected to appear in criminal court in Manhattan later Tuesday morning. The charges don't stem from him using the firearm in a menacing manner but of possessing a gun he wasn't registered to have, according to the spokesman.
Felton, 29, turned himself in at 12:50 a.m. Tuesday and was questioned at the 20th Precinct in the Upper West Side of Manhattan, hours after the Knicks' loss to the Dallas Mavericks, the spokesman said.
Felton signed a three-year, $10 million contract with the Knicks prior to the 2012-13 season.
He has struggled this season, and the Knicks offered him in several trade packages prior to the Feb. 20 trade deadline but could not complete a deal.
New York City has strict gun possession laws.
In 2009, New York Giants wide receiver Plaxico Burress was sentenced to two years in prison after accepting a plea deal on a firearm charge following an incident in which he suffered a self-inflicted gunshot wound to his thigh when his gun accidentally went off in a Manhattan nightclub. He faced a minimum sentence of 3½ years if convicted at trial.
Information from The Associated Press contributed to this report.