The attack occurred at the Grand Mosque in the small town of Salmossi in the Oudalan region.
One source said 13 people died instantly while three more succumbed to their injuries later. Two more are still in a critical condition.
"Since this morning, people have started to flee the area," one resident from the nearby town of Gorom-Gorom said.
He added that there was a "climate of panic despite military reinforcements."
Later on Saturday, roughly 1,000 people marched in the capital Ouagadougou "to denounce terrorism and the presence of foreign military bases in Africa."
"Terrorism has now become an ideal pretext for installing foreign military bases in our country," Gabin Korbeogo, one of the organizers of the march, said.
He added: "The French, American, Canadian, German and other armies have set foot in our sub-region, saying they want to fight terrorism. But despite this massive presence... the terrorist groups... are growing stronger."
The attack at the mosque over the weekend is part of wider conflicts in Burkina Faso, as its battle to control ongoing violence becomes ever more difficult.
Until 2015, the West African nation was largely spared the violence that was notorious in neighboring Mali and Niger. But since then terrorists linked to various terror networks have begun to infiltrate Burkina Faso.
Guerrilla hit-and-run tactics combined with mines and suicide bombings have resulted in the deaths of almost 600 civilians in recent years, according to AFP. Attacks are becoming an almost daily occurrence.
In addition, several hundred thousand have fled their homes because of the violence and half a million people no longer have access to health care.