Several other people were wounded in the attack which took place in the village of Foutouri in the Est region of the country.
The identity of the gunmen is not yet clear but the area has come under attack over the past year from suspected jihadist groups with links to al Qaeda and Islamic State.
Burkina Faso President Roch Marc Christian Kabore tweeted: “I condemn the barbaric attack against the Protestant Church of Hantoukoura in the department of Foutouri, which left 14 dead and several wounded.
“I offer my deepest condolences to the bereaved families and wish a speedy recovery to the wounded.”
An Islamist insurgency in Burkina Faso this year has ignited ethnic and religious tensions, leaving large parts of the country ungovernable, especially in northern areas bordering Mali.
Last month, gunmen opened fire on a convoy of buses carrying mine workers in the Est region, killing 39 people.
The timing of Sunday’s incident, during hours of worship, mirrors other attacks on Christians this year – a new phenomenon in a West African country that has long prided itself on its religious tolerance.
Burkina Faso was once a pocket of calm in the region, but the past year’s violence has killed hundreds and forced nearly a million people from their homes.