A Red Cross official said all 11 people on board were killed.
Witnesses said the aircraft was from the Uganda military, with an airport worker identifying it as a cargo jet.
"I saw the plane on fire ... One of the wings exploded in the air... When it hit the ground, another explosion occurred," Hassan Mahamud Jama, a resident, told Reuters.
Friday's clashes come despite elders from an influential clan saying they had agreed a ceasefire with Ethiopian troops that was set to begin on Friday afternoon.
"There was peace... in Somalia for six months while the Union of Islamic Courts were in power"
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The truce was set to take effect at 12pm (09:00GMT), said Uwas Abdi Dahir of the Hawiye clan, who was involved in the negotiations.
Ethiopian military officials confirmed that they had met clan elders but stopped short of saying a truce had been agreed.
At least 16 people have been killed and hundreds wounded this week in the bloodiest clashes since the government forces seized the coastal city from Union of Islamic Courts three months ago.
Al Jazeera shut
The Somalian government has ordered Al Jazeera and two local private radio stations to stop broadcasting from the country's capital.
A government spokesman said the broadcasters had "violated the ethics of the media by misinforming about the reality in Somalia".
Hussein Mohamed Muhamoud said did not give specific incidents in which the organisations violated media ethics.
Al Jazeera expressed disappointment at the decision on Friday, closing its Mogadishu office but continuing to cover events in Somalia from other sources and locations.
Al Jazeera Network issued a statement saying: "Al Jazeera, while expressing its disappointment, re-asserts its commitment to the principles of the free press."
The network said it defendeds "the right of viewers to know what happens across the world with impartiality and integrity."
On Friday, Al Jazeera continued to broadcast the latest pictures to come out of the capital.