The company spokesman said all 11 people on board, including seven crew members, were killed.
The plane was downed Friday, after it had delivered equipment for Ugandan peacekeepers in Mogadishu.
Last week, another Belarusian transport plane was attacked in the capital Mogadishu.
The Il-76 airliner, which was carrying humanitarian cargo as part of a UN mission, was hit by a grenade or missile fired from a small boat while landing.
The crew and nine people on board were not injured, and the plane, which was at an altitude of 150 meters (450 feet) when it was hit, managed to land despite a heavily damaged fuselage.
Transaviaexport delivers humanitarian aid to many countries, including Iraq and Afghanistan.
Mogadishu has been plagued by violence since former President Mohamed Siad Barre was ousted in 1991. The civil war-torn East African state, which has no recognized central government, has also struggled to cope with famine and disease relying on UN aid.