Another four soldiers are missing after the attack reportedly carried out by a jihadist group in the Yagha region, near the Niger border.
Burkina Faso is involved in a regional effort, together with Mali, Niger, Mauritania and Chad, to fight the jihadist uprising in the West African Sahel region.
However, Burkinese security forces have not been able to prevent the violence, despite the help of France which has about 5,000 soldiers in the region.
According to the UN, nearly 4,000 people were killed last year in jihadist attacks in Burkina Faso, Mali and Niger. About 800,000 people have been on the run since 2015.