"August 19th is a dark stain on the life of our national army," said President Roch Marc Kabore in a statement.
"It is a heavy toll, which ... saddens us," he added.
Seven other soldiers were wounded and five are missing, he said in the statement.
The army launched an army and air force operation to find the culprits.
- Burkina Faso declares partial state of emergency
- Jihadist group claims attacks on French interests in Burkina Faso
Although Burkina was considered a stable country within the Sahel region, insurgency from within over the past three years as well as some jihadist violence exported froml its neighbor, Mali have created strife.
The opposition Union for Progress and Change (UPC) party has called for the government to step down after this latest attack, accusing them of failing push out jihadists and protect its citizens.
"It's a team overwhelmed by the turn of events, which is currently crossing its arms, waiting for how fate will play them and the Burkinabes," said UPC in a statement.
Some 150,000 people have fled the region and hundreds have been killed.
The government had issued a state of emergency in a number of northern regions near Mali, including Soum, last December.