A contingent of troops came across "a complex, large-scale attack" in the East region which also left 12 soldiers wounded, according to an army statement.
The soldiers "neutralised at least 40 terrorists before the arrival of reinforcements" during the "particularly intense fighting", it added.
The wounded troops have been evacuated and are being treated by the health services, the army said.
Burkina Faso has been grappling with a bloody jihadist insurgency since 2015, when unrest spilled over from neighbouring Mali.
Fighting between the security forces and groups linked to Al-Qaeda and the Islamic State group has left thousands dead and forced millions of people to flee their homes.
Anger within the military at the government's failure to stem the jihadist attacks sparked two coups in 2022. Around 40 percent of the country's territory lies outside state control.
Captain Ibrahim Traore, who has led the West African nation since seizing power last September, this month signed a decree for a year-long "general mobilisation" to give the state "all necessary means" to counter the militants.
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