The multinational force said on Twitter that vehicles and equipment were destroyed in the morning assault on the al-Shabab camp outside Afmadhow and "a large cache of weapons" was captured. The statement said helicopter gunships supported the attack.
A separate statement by Kenya's defense ministry said an unknown number of extremists were injured. There was no immediate word of casualties among the AU or Somali forces.
Al-Shabab has lost ground in Somalia in recent years under pressure from such assaults but continues to carry out deadly attacks in the capital, Mogadishu.
The group has responded angrily to the election last month of new President Mohamed Abdullahi Mohamed, during whose brief term as prime minister the group was expelled from Mogadishu.
Mohamed has vowed to make security a priority in the fragile Horn of Africa nation, which is trying to set up its first fully functioning central government in a quarter-century.
But the expected withdrawal of the AU force, which numbers more than 20,000, by the end of 2020 has caused concern, as the burden of fighting al-Shabab would fall on national forces that observers say are not yet ready.
The United States military is pursuing a larger role in Somalia, where it already carries out drone strikes and has special forces advising local troops. The deadliest assault on al-Shabab so far was in March 2016, when a U.S. airstrike struck a training camp, killing more than 150 fighters.