Sgt. Robert Eberling of the Grapevine, Texas, Police Department told the Chicago Tribune Melton was booked on misdemeanor assault and public intoxication after the Sunday morning incident.
Eberling told the newspaper Melton "became belligerent with some of the staff members of the restaurant. He was asked to leave. When he was in the process of being escorted from the restaurant, he struck one of the staff members. He was restrained at that point."
Police alleged Melton punched the bar's manager in the face and bit him on the arm, requiring restraint by four staff security members.
He was released from jail after posting bond, the Tribune reported.
"We are aware of the reports regarding Henry Melton," the Bears said in an issued statement. "We are currently gathering information to learn more about the circumstances surrounding the arrest."
Melton, 27, hasn't played since September after suffering a season-ending knee injury. He has 89 tackles and 15 1/2 sacks in four seasons for the Bears.