Two other security sources told AFP jihadists were behind the attack.
“The attacks took place almost simultaneously,” said Mohamed Dah, Soum police high commissioner. “Gunfire has ceased but the assailants are still at the scene. We’ve dispatched military reinforcements.”
Another security source, who did not wish to be named, said the attack at one post began when “a dozen jihadis arrived on six motorbikes”.
The incident comes with the capital Ouagadougou on high security alert as it hosts the 25th Pan-African Film and Television Festival, with scores of cinephiles and international visitors in town.
Long spared the Islamist violence affecting several nations in the region, notably Mali and Niger, Burkina has been hit by a series of attacks and kidnappings since April 2015.
Most of the raids have occurred near the northern border, but in January 2016, 30 people were killed and 71 wounded in the capital Ouagadougou after gunmen stormed a restaurant and a four-star hotel, taking hostages.
Al-Qaeda in the Islamic Maghreb claimed responsibility for the attacks, which ended after Burkinabe troops and French counterterrorist forces posted in the country staged an offensive.
On December 12, jihadists killed 12 soldiers in an attack against an army squad about 30 kilometres (19 miles) from the Mali frontier.
The raid — the deadliest ever against Burkina Faso’s military — caused a public outcry, with some calling for the sacking of a military leadership accused of failing to match up to the jihadist threat.