During cruise flight at 37,000 feet over the Gulf of Mexico, the scheduled international passenger flight encountered severe turbulence after inadvertently penetrating rapidly developing convective formations. One of the flight attendants was seriously injured. When the turbulence encounter occurred, the flight crew was attempting to deviate around cloud formations. The flight crew reported that the seat belt sign was illuminated prior to the turbulence encounter and that the captain made an announcement to the passengers reminding them to remain seated with their seatbelts secured. It is unknown whether the flight attendant was seated or standing, or where she was positioned at the time of the event. Following the turbulence encounter, the flight diverted to a nearby airport and landed without further incident. Probable Cause: the flight crew’s inadvertent encounter with convective turbulence while in cruise flight. A factor was the rapidly developing convective activity.