Initial reports said the aircraft, an Antonov An-2, which belonged to a small military air force school, was carrying 11 people.
"The aircraft ... which was on a flying mission for parachuting training crashed on Monday," the defense ministry said in a statement. "Ten military people lost their lives in the air catastrophe and three were injured."
The aircraft was carrying a crew of four and nine members of the naval forces, the statement said.
The plane crashed shortly after take-off and caught fire when it hit the ground, the ministry said. Firefighters put out the flames around 35 minutes later.
The three survivors were taken to the emergency hospital in the city of Constanta, 20 km (12 miles) from the crash site, and were in critical condition, a doctor coordinating the rescue told the local television station Realitatea.
Defense Minister Gabriel Oprea has appointed a commission to investigate the cause of the crash.
