A gunman opened fire during a service on Sunday, with reports that the pastor and children were killed.
Illia Djadi, Christian charity Open Doors' Senior Analyst on West Africa told Premier they were likely killed because they were Christian and that the killer was probably an Islamist militant, given the nature of previous attacks this year.
Jihadist groups have killed hundreds of people in the last year, especially near the border with Mali.
"The church and the Christians in Burkina Faso are really traumatised, actually they are overwhelmed," Illia Djadi said.
"They used to live peacefully with other religious or ethnic communities."
Pastor Samuel Sawadogo, who cares for displaced Christians in the city of Kaya, said: "We don't know who the attackers are,
"All we know is that they attack Christians. We are troubled and filled with pain over the deaths of our family members."
President Roch Marc Christian Kabore said he condemned "the barbaric attack" in the town of Hantoukoura.
He said several people also were wounded.
In a tweet, Mr Kabore offered his "deepest condolences to the bereaved families" and wished "a speedy recovery to the wounded".
Open Doors, who campaign on religious freedom, said 41 Christians have been killed in the country this year in violent attacks and that pastors and their families have been abducted.
Islamic extremists have been active in Burkina Faso since 2015.
Jihadists have attacked police stations and churches across the country's north but also recently have struck in the east.
In October, gunmen generally believed to be Islamic extremists attacked a convoy carrying employees of a mining company in that region, killing at least 37 people.
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