47-year-old Claudel Barrau, who apparently took the photo with his cell phone camera, faces departmental charges of no cell phone in jail and no photographs in jail.
Possession and use of cell phones in jails, even by guards, is prohibited.
Officials say both officers were removed from their posts at the North Infirmary Command, formerly the Rikers Island Hospital, last Wednesday.
They were transferred to other assignments and placed were on modified duty, pending departmental hearings.
Senior department officials acted after the photo, taken by Barrau, began circulating among correction officers last week.
Officials determined Green's identity and verified the photo was taken on Rikers before taking action.
They are looking into why Green was sleeping and why Barrau took the photo of his fellow officer.