Four of the six crew members on board the aircraft – carrying ammunition for international forces fighting Islamist militants – were killed.
Ammunition could be heard exploding inside the plane as the fire spread, closing the airport. The blaze was put out after about two hours.
Ethiopian troops entered Somalia in 2011 to assist African Union forces.
It is not known yet when the plane got into difficulties, and whether it overshot the runway, or fell short of it.
It was not immediately clear where the plane flew from.
The Somali Islamist militia, al-Shabab, which is linked to al-Qaeda, described the crash as an act of God, reports the BBC’s Abdullahi Abdi Sheikh in Nairobi.
On its Twitter feed, al-Shabab said the plane crash had “thwarted… the plots of the enemy invaders”.
Ethiopian troops are not part of the African Union peacekeeping force, supporting the Somali government forces in their fight against al-Shabab.
Al-Shabab militants have shot at planes in the past but not in recent years, the Associated Press news agency reports.
The two crew members injured in the crash are currently receiving medical attention at the African Union hospital in Mogadishu, its mission in Somalia, Amisom, said in a statement.
Crash probe
The crash occurred shortly before 08:00 local time (05:00GMT), Amisom said. There was no damage to the runway, it added.
“The cause of the incident is yet to be established but investigations are currently under way,” the AU mission said.
The aircraft was a Soviet-made Antonov 24, Reuters news agency reports. Military aircraft regularly land at the airport. It was unclear what ammunition the plane was carrying.
A convoy of empty Somali military trucks had been seen earlier at the airport, Reuters adds.
Somalia – which has seen conflict since 1991 – has a poor record on aviation safety.