A policeman and four militiamen were also killed in the fighting, said Captain Anthony Mualushayi, the army's spokesman in the Beni region.
The term "Mai-mai' is widely used to describe armed groups claiming to represent communities in the region's many ethnic feuds.
Separately, the Allied Democratic Forces (ADF) on Wednesday killed four women and three men as they worked in fields near the Ugandan border, Ricardo Rupande, a community organiser in Rwenzori, told AFP.
The ADF is a group that the self-described Islamic State group says is an affiliate.
The same night, ADF members set fire to a medical centre in the village of Luonoli, "reducing it to ashes," Luonoli village chief Semu Kiheka told AFP, adding that local people fled after the attack.
The ADF is the most violent of more than 120 armed groups that roam eastern Democratic Republic of Congo, according to monitors.
The group is accused of killing thousands of people in a years-long campaign in the region, and of orchestrating recent attacks in the Ugandan capital Kampala.
On 30 November, Ugandan troops began to deploy across the border, joining Congolese troops in a crackdown on the ADF in the Beni region.