A statement issued by the Browns indicated team employee Eric Eucker killed himself Saturday at the club's facility in Berea, Ohio.
A Cuyahoga County Medical Examiner spokesman told NFL.com Eucker was found dead of apparent hanging in a maintenance shed.
The incident came the same day Kansas City linebacker Jovan Belcher shot himself to death at the Chiefs' practice field after killing his girlfriend at the home they shared.
"This is a terrible tragedy and our heartfelt condolences go out to Eric's family," the Browns' statement read. "Eric was a good friend and colleague, and an outstanding employee. He will be missed by everyone in the Cleveland Browns organization."