The British singer, whose real name is George O'Dowd, claimed his home had been burglarized around 3 a.m. Friday, said Detective Kevin Czartoryski, a police spokesman.
Officers arrived at O'Dowd's Manhattan apartment and discovered a small amount of cocaine next to a computer, police said. Police were continuing to investigate.
Barbara Thompson, a spokeswoman for the Manhattan District Attorney's office, said O'Dowd was still in police custody and was awaiting arraigment Friday evening. He was yet to be charged.
A former spokesman for O'Dowd's autobiographical musical "Taboo," which closed last year, said he did not know whether the singer had a spokesman or lawyer.
It is not the first time Boy George has had problems with drugs.
In 1986, the singer 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."