The fuel truck driver indicated that he had been waiting 10-15 minutes for the flight to arrive and that the truck was in neutral with no emergency brake set. He stated that he had his foot on the brake but that he closed his eyes briefly and fell asleep and was unaware of what happened until the fuel truck collided with a parked airplane that had just arrived at the gate. One of the two flight attendants received a minor injury; there were no injuries to the other crew members or the passengers. The airplane received substantial damage to the aft portion of the fuselage where the fuel truck impacted.