The singer, whose real name is George O'Dowd, claimed his home had been burgled at about 3am on Friday, said Detective Kevin Czartoryski, a New York Police spokesman.
Officers arrived at O'Dowd's apartment and discovered a small amount of cocaine next to a computer, police said. Police were continuing to investigate.
The singer was released without bail after being charged with fourth-degree criminal possession of a controlled substance, allegedly more than an eighth of an ounce (five grams) of cocaine, said Barbara Thompson, a spokeswoman for the Manhattan District Attorney's office. The charge carries a maximum penalty of five to 15 years in prison.
Calls to the office of O'Dowd's lawyer went unanswered early today.
It is not the first time that Boy George has had problems with drugs.
In 1986 he was convicted for heroin possession in England. Two of his friends overdosed in the incident and O'Dowd was forced into a rehabilitation program. The conviction led to the disintegration of his group, Culture Club, one year later.
Boy George, famous for his androgynous persona, and Culture Club, had hits including Karma Chameleon and Do You Really Want to Hurt Me.