Moussa Faki Mahamat, chairperson of the African Union Commission, wished the injured a speedy and full recovery following an attack in Balad district, located about 30km northeast from the capital city of Mogadishu.
"We are united in grief with the families of the fallen soldiers, the people and Government of Burundi for the loss of the brave troops who made the ultimate sacrifice in service of, and support to a fellow African nation in combating terrorism," Mahamat said in a statement.
Floribert Biyereke, Burundian army spokesman, confirmed the death of six soldiers, adding that three others were also injured seriously during the attack.
Biyereke said two other soldiers, who were part of the African Union peacekeeping mission, were also missing after the attack.
Mahamat said the AU remains committed to working with the Somali government to further consolidate peace and security in the country.
He called on the international community to provide appropriate support to Somalia and African Union Mission in Somalia to consolidate security gains in the country.
Despite being driven out of Mogadishu, the al-Shabab group still stages guerrilla-style assaults and bomb attacks to drive out AU mission's troops from Somalia and impose its harsh version of Islamic law across the Horn of Africa nation.