American Airlines flight 2401 encountered severe turbulence while in cruise flight at FL310 and a flight attendant fractured his ankle. The captain was the pilot flying (PF) and the first officer was monitoring. Ride conditions were smooth with no reports of turbulence in the area and the crewmembers had the weather radar turned off. The flight was in day visual meteorological conditions (VMC) with the visibility greater than 20 miles. About 20 miles NW of the REDFN waypoint, near airway Q105, the flight experienced a single “jolt” of severe turbulence, which caused the autopilot to disconnect, and the airplane to roll about 30 degrees to the right and climb about 300 feet. The PF took control and returned the airplane to its assigned altitude and reengaged the autopilot. When the turbulence occurred beverage service had recently concluded, and two flight attendants were in the aisle collecting trash. One flight attendant was in the aft galley securing service items and was thrown to the ceiling and fell, fracturing his left ankle. Ten passengers who were not seated or who were not using their seatbelts sustained minor injuries. The fasten seatbelt indication to passengers was turned off.