The violence took place on Sunday in the village of Silgadji, not far from the volatile border with Mali.
Urbain Kabore, the communications director for the Sahel region of Burkina Faso said the attackers arrived on motorbikes at the end of a Sunday service and killed the pastor, two of his sons and three other worshippers.
There was no immediate claim of responsibility although violent Islamic extremism has been increasingly destabilising the country. A number of jihadist groups are known to operate the area.
However, it is the first attack on a church since jihadist violence erupted in the West African country in 2016.
Meanwhile, authorities said that in a separate incident attributed to jihadists in the east of Burkina Faso, five teachers were shot dead on Friday.
The Islamic extremists have also targeted foreigners, abducting and killing a Canadian geologist earlier this year
It is still not known whether a Catholic priest kidnapped a month ago is still alive.
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