Two more men were missing after around 40 jihadists riding pick-up trucks and motorbikes attacked the army's Nassoumbou base.
"A detachment of our army's anti-terrorist force suffered a murderous attack which claimed the lives of 12 of our valiant soldiers and left some wounded," said President Roch Marc Christian Kabore, in an address to the nation.
"I strongly condemn this horrible attack which shows the cruelty of these perpetrators," added Kabore, who did not specify the number of injured.
Two more men were missing after around 40 jihadists riding pick-up trucks and motorbikes attacked the army's Nassoumbou base some 30 kilometres (18 miles) from the Burkina-Mali border, the high commissioner of Soum province, Mohamed Dah, earlier told AFP by phone.
"They were heavily armed with Kalashnikovs and rocket-launchers. They opened fire at the depots, the tents and set fire to some of the vehicles," he said, adding that it was "the biggest jihadist attack ever perpetrated" against the army.
Dah added that at least five attackers were killed although their bodies were removed from the scene by other assailants on motorcycles.
A security source who asked not to be named said the assailants were wearing turbans and waving black jihadist flags.
Troops at the Nassoumbou base are part of a 600-strong anti-terrorist battalion that was deployed in January 2013 when France sent in troops to counter a jihadist insurgency in northern Mali.
This was the second direct attack against the Burkina army since jihadist assailants surfaced in the country in early 2015, mostly staging attacks in the north near the borders of Mali and Niger.
But in January this year, three jihadists left dozens of people dead and 71 injured in an attack in the heart of the capital.
Thirty people were killed when gunmen stormed the four-star Splendid Hotel and a nearby cafe in Ouagadougou.
The army has, since 2012, had an anti-terrorist battalion deployed along the country's long border with Mali, an area which is frequently subjected to attacks and kidnappings.
In October, Kabore had called on his countrymen to help fight back against the mounting jihadist threat.