The Captain stated that the airplane encountered light-to-moderate turbulence on climb-out. The cabin seat belt signs were illuminated, and the flight attendants were briefed to remain seated. The airplane weather avoidance radar was on and no significant weather was present on the radar screen. An overhead compartment had opened up in the cabin area, and a flight attendant got up to secure the compartment. The airplane encountered a couple seconds of intense moderate turbulence, and the flight attendant collided with the cabin overhead panels. The flight diverted to another airport to obtain medical treatment for the injured flight attendant. Review of the digital flight data recorder revealed the airplane experienced a vertical excursion of 1.9 g's.