The incident occurred Nov. 19, eight days after Winslow's four-game suspension for violating the NFL's policy on performance-enhancing substances expired.
Winslow is charged with possession of a controlled dangerous substance, a third-degree offense. If convicted, he faces up to five years in prison.
"We are aware of the situation," a team spokesperson said in a statement to NFL Media on Thursday. "This is a pending legal matter and we will have no comment."
This arrest is a substance abuse issue, which doesn't fall under the same umbrella as his October suspension.
It's not known if Winslow is already in the NFL's substance abuse program for previous offenses.
An impending free agent, Winslow's status with the Jets is up in the air. The arrest won't help his chances of re-signing after spending the entire 2012 season out of the league.