Maman Sidikou, the head of the AU in Somalia, apologised to the families of the seven people killed in the attack.
The AU had previously denied that the incident took place.
According to the campaign group Human Rights Watch, AU troops from Uganda began shooting at men at a wedding party after coming under fire.
Witnesses said that the troops entered several houses in Merca, 70km (45 miles) south of the capital Mogadishu, after a grenade attack on their convoy.
Mr Sidikou admitted on Friday that seven civilians had been killed.
"We have established that, on that occasion, seven civilians died following an incident involving our troops," he said in a statement.
"I would like, on behalf of the African Union, to offer my sincere apology for these deaths. We regret these deaths," he added.
The three AU soldiers have now been indicted and are waiting to be arraigned, according to the statement.
"I have instituted a board of inquiry composed of military, civilian and police officers who are not from the contingent concerned in order to ensure impartiality," Mr Sidikou said.
Witnesses described the incident to Human Rights Watch.
"At one house, where the Moalim Iidey family was celebrating a wedding, the soldiers separated the men from the women and shot the six adult men - four brothers, their father, and an uncle," HRW said in a statement.
"Four died immediately, one brother hid under a bed after being shot but later died, and the father died during the night after the soldiers allegedly refused to allow the family to take him to the hospital," it said.
HRW says witnesses also allege that 11 civilians were killed by AU troops on 21 July in Merca.
None of the survivors of the two alleged incidents spoken to by Human Rights Watch have yet been interviewed by AU investigators, the rights group said.
AU troops have been in the Somalia since 2007 helping various UN-backed governments fight the al-Shabab militant group.
"Our soldiers are operating in a very complex environment," Mr Sidikou said in the AU statement.
"We will continue to appeal to our host communities to facilitate the work of our troops in the fight against al Shabab."
Three Ugandan soldiers have been charged over the killing last month of a group of civilians in Somalia, an African Union (AU) official has said.