The town’s mayor, Ousmane Zongo, said that there was panic as other buildings were burned down and a health centre looted.
Jihadist violence has flared in Burkina Faso since 2016, and this is the third attack on a church in five weeks.
How did the attack unfold?
It began at about 09:00 (GMT and local time), during Mass.
The mayor of Dablo, Mr Zongo told the AFP news agency: “Armed individuals burst into the Catholic church… They started firing as the congregation tried to flee.
“There is an atmosphere of panic in the town. People are holed up in their homes, nothing is going on. The shops and stores are closed. It’s practically a ghost town,” he said.
Security sources told AFP that reinforcements were being sent from Barsalogho, some 45km (30 miles) to the south.
A local journalist told the BBC those killed included church elders and that residents were angry that soldiers in a nearby base did not respond promptly.