The attackers looted and burned down the house of Revd Nicolas Guerekoyame-Gbangou, the chairman of CAR's Evangelical Alliance, in the country's capital Bangui.
Revd Guerekoyame-Gbangou wasn't in at the time the extremists came, and his family managed to escape before they were attacked.
The armed gunmen murdered two other people taking refuge in the house.
The attack on Revd Guerekoyame-Gbangou was part of ongoing sectarian violence between Christians and Muslims in the country, after the body of a Muslim man was found in Bangui earlier this year.
At least 100 people have died in the fighting, and around 30,000 are currently displaced in CAR from current and previous political and religious fighting.
CAR is due to have political elections on October 18, however it's uncertain whether these will take place given the current violence.
An Africa advocacy officer for anti-persecution charity Christian Solidarity Worldwide, who can't be named, told Premier: "The interim government [and] the UN peacekeeping forces in the country have barely been able to hold complete authority across the country.
"So what really needs to happen is the armed groups... need to be fully disarmed and rehabilitated back into the community.
"We're calling for there to be adequate protection not just for Revd Nicolas but also the Catholic archbishop and the chief imam in the country who jointly have established an interfaith peace platform."
About three quarters of CAR are Christians.
You can listen to Premier's Aaron James speak to CSW's Africa Advocacy Officer here:
