The transporter was carrying more than 90 people, mostly troops, when it overshot the runway on Jolo island.
The dead are mainly military personnel, but three civilians on the ground were also killed, the defence ministry said.
Rescue workers scoured the wreckage of the Lockheed C130 Hercules in a wood near several buildings.
The aircraft burst into flames on crashing, sending a large black cloud into the air.
Several dozen people were injured, and five are still missing, the military said. A nearby military hospital treated survivors.