The fighting broke out in the town of Djibo on Sunday morning.
"A gendarmerie unit and a reconnaissance mission team were ambushed. Sadly a soldier was killed during the attack," the military statement said.
The two units managed "to neutralise six terrorists," it added.
Army chief Moise Miningou, in the same statement, said five other troops were killed on Thursday also in the north.
Burkina Faso's northwest border is with Mali, and to the northeast is Niger, with all three countries fighting a long-running jihadist insurgency.
According to UN figures, jihadist attacks in Burkina Faso, Mali and Niger left nearly 4,000 people dead last year, including 800 in Burkina Faso alone.
Some 800,000 people have been displaced since 2015.
The poorly-trained and badly-equipped Burkina security forces have been unable to stem the violence despite help from abroad, notably from France which has 5,100 troops taking part in the Barkhane anti-jihadist force in the Sahel region.
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