The incident happened on Wednesday near Tibou in Loroum province bordering Mali, when the convoy of trucks came under attack by around 100 armed men, it said.
Two military units that had been escorting the convoy counter-attacked, "neutralising at least 50" assailants, it said in a statement. Two civilians who were on the convoy were also killed.
The military's account could not be independently verified.
The landlocked Sahel state is struggling with a seven-year-old jihadist insurgency that began in neighbouring Mali.
More than 10,000 civilians and military have died, according to NGO estimates, while more than two million people have fled their homes. Around 40 people were killed at the weekend in two attacks near Bourasso.
Burkina has been ruled since 2022 by a junta led by Captain Ibrahim Traore, who has vowed to recapture the 40 percent of the country's territory that remains outside the government's control.
He has also promised a return to democracy with presidential elections by July 2024.
On Tuesday Prime Minister Apollinaire Kyelem de Tambela told parliament that the authorities would "never negotiate (with the jihadists), either over Burkina Faso's territorial integrity or its sovereignty."
"The only negotiations that matter with these armed bandits are those taking place on the battlefield," he said.
But de Tambela suggested that attacks could see the electoral timeframe pushed back.
"We cannot organise elections without security. If you have a magic wand to ensure we can hold elections as soon as possible, we'd do it," he said.
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