The soldiers were charged for the shooting incident in November 2010 and in January that resulted in civilian injuries in Mogadishu and were sent back home to serve their sentences.
"These regrettable incidents have now been fully investigated with the help and assistance of the civil police and medical authorities," the force commander Major General Nathan Mugisha said on Tuesday.
"The soldiers involved have now faced the due process of law and been punished. Their sentences illustrate that any acts of carelessness and irresponsibility will not be condoned or tolerated."
The 9,000-strong AU force that first deployed in Mogadishu in 2007 to protect Somalia's transitional government has been accused in the past of indiscriminate shelling in reprisal attacks against hardline Shebab rebels.
But it has denied targetting civilians, who have borne the worst brunt of the bloody clashes between the AU troops and the Shebab, an Al Qaeda-inspired militia.
The force said that its inquiry found that no civilians died in the shooting by the convicted soldiers.
"Sadly, accidents such as these will occasionally happen. They are deeply regrettable and deplorable," Mugisha said.