Sheikh Muktar Robow Mansoor, al-Shabaab's spokesman, said a bomber wearing a jacket with explosives had detonated his charge near the compound and another in a car had set off his device at the gate.
Soldiers from Burundi are stationed in the camp that was targeted.
The AU force denied there was a suicide attack, saying that a compound had come under fire from mortar shells.
Major Barigye Ba-Hoku, a spokesman for Amison, or the African Union peacekeeping mission to Somalia, said they were "yet to find out the impact of the shelling."
Amison has 3,500 soldiers from Burundi and Uganda stationed in Mogadishu.
Peacekeepers have often been targeted by anti-government fighters since the first Ugandan contingent was deployed in the country in March 2007.
Ethiopian forces who had borne the brunt of the armed uprising, pulled out of Somalia last month, sparking fears of a security vacuum.