Jeffrey Epstein was moved to a suicide-watch unit in a New York City detention center after the financier facing sex-trafficking charges was found unconscious in his cell Tuesday morning, according to people familiar with the matter.

Mr. Epstein, 66 years old, is being held pending trial at the Metropolitan Correctional Center in Manhattan. He faces two counts related to alleged sex trafficking of minors.

He was arrested July 6 at Teterboro Airport in New Jersey as he was returning from Paris on his private jet. He has pleaded not guilty to federal charges stemming from an alleged scheme to exploit underage girls and faces a maximum sentence of 45 years in prison.

Officers at the Metropolitan Correctional Center discovered Mr. Epstein unconscious in his cell, according to people familiar with the incident. He had marks on his neck, the people said, but officials said his injuries weren’t life-threatening.

Mr. Epstein’s lawyers didn’t respond to requests for comment.