It took place during Sunday worship in Essakane village in Oudalan province – close to the border with Mali. Few details have been given.
A church official indicated the gunmen were suspected Islamist militants.
There was no immediate response from the authorities in the West African country’s capital, Ouagadougou.
A statement by the head of the local diocese, Abbot Jean-Pierre Sawadogo, said 12 people were killed instantly, while three others died at the hospital.
“In this painful circumstance, we invite you to pray for those who died in faith, for the healing of the wounded, and for the consolidation of grieving hearts,” the statement reads.
It is the latest atrocity in the country to be attributed to Islamist militants.
More than a third of Burkina Faso is currently under the control of insurgents.
The authorities have been battling Islamist groups linked to al-Qaeda and Islamic State, which have taken over large swathes of land and displaced millions of people in the Sahel region.
In the last three years, churches have been targeted and scores of worshippers killed.
Burkina Faso, which is ruled by a military dictatorship, recently pulled out of the regional political and economic bloc, Ecowas, along with its Sahel neighbours, Mali and Niger.
They cited lack of support from Ecowas in the fight against terrorism as one of the reasons for wanting to exit the union.
The three junta-led countries had already been suspended from the bloc, which had been urging them to return to democratic rule.
Earlier this month, Burkina Faso’s military-backed president Ibrahim Traoré said Russian troops could deploy to fight jihadists in the West African country if needed.
