Police responded to a 911 call about a domestic dispute at Cunningham's Summit, N.J., home on Dec. 29, the Union County prosecutor's office said in a statement.
After an investigation, Cunningham was charged with third-degree invasion of privacy for the disclosure of sexual images without the consent of the person in the images, as well as criminal mischief for the destruction of clothing.
No further details were given about either charge. The prosecutor's office said a woman had lived at the home with Cunningham until recently.
The police officers also received permission from Cunningham to search the fifth-year player's Audi, where they found a loaded .380-caliber handgun in the glove compartment. He was charged with fourth-degree unlawful weapon transport.
Cunningham was released without bail, with a court hearing pending.
The Jets said in a statement: "We are aware of the situation. This is a pending legal matter and we will have no comment."
Drafted by New England in the second round back in 2010, Cunningham started 11 games that season but didn't make much of an impact. He hasn't seen much playing time since and spent all of the 2014 season on injured reserve with a torn Achilles' tendon.
He will be an unrestricted free agent in March.