An AU spokesman in the city said the aircraft had been carrying troops from Burundi.
"The insurgents did what they have been doing. They fired mortars shortly after a plane carrying our supplies landed, but there were no casualties," Baridgye Bahuko, spokesman for the AU mission in Somalia, said.
"I don't think that the AU forces randomly fire at civilians in residential areas, though we have the right to defend ourselves from those who attack us."
The 2,000 AU peacekeepers are mostly based at the airport due to the violence in the capital.
Civilians bore the brunt of the fighting with at least four residents killed and seven injured when one shell detonated in the Kilometre 4 area of Mogadishu.
"A group of local teenagers was sitting playing cards here under a big tree," Abdullahi Farah, a witness, told the Reuters news agency. "Now their flesh is scattered everywhere."
Said Nur Farah, a Mogadishu resident, said that his brother was one of the people killed in the clashes.
"We collected his body from under a tree," he said. "He had been talking to friends when the shell landed."
An official at the city's main Madena Hospital said about 50 wounded civilians had been admitted. Two of them, including a two-year-old child, later died of their injuries.
Armed groups opposed to the transitional government and the Ethiopian presence in Somalia carry out near-daily attacks across the country.
Fighting has killed more than 9,500 civilians since the start of last year, and an unknown number of armed men. More than one million people have been forced from their homes.