The UN on Friday said 37 deaths were confirmed in Alindao, while some 20,000 people were affected by the violence, which forced "thousands" to flee.
"This vicious cycle of repeated attacks against civilians is unacceptable. Civilians want security, peace and a future," said Najat Rochdi, UN humanitarian coordinator in the CAR.
One of the world's poorest nations despite a rich supply of diamonds and uranium, the CAR has struggled to recover from a 2013 civil war that erupted when President Francois Bozize, a Christian, was overthrown by mainly Muslim Seleka rebels.
In response, Christians, who account for about 80 percent of the population, organised vigilante units dubbed "anti-balaka". [In essence, the Christians committed genocide against Muslims.]
Alindao is a stronghold of the Union for Peace in CAR (UPC) Muslim militia that has its roots in the Seleka group. It has witnessed chronic fighting in recent months that has also killed two UN soldiers and a humanitarian aid worker.
Earlier, Vladimir Monteiro, spokesman for the UN peacekeeping mission Minusca, told AFP that the Christian anti-balaka had killed Muslims and an hour later, "the UPC responded by attacking a camp for displaced people" in Alindao.
Alindao lies on a critical route traversing the south and east of the country and is in the heart of a region numerous gold and diamond mines that have helped fuel the conflict.
In September, the UN warned of a "disastrous" humanitarian situation in the region, which it said was under the control of armed groups.
The country of 4.5 million people has been blighted by simmering sectarian violence since 2013 that has killed thousands.
The state controls only a small part of CAR's national territory. Armed groups clash in the provinces for control of resources, including diamonds, gold and livestock.
The UN has around 12,500 personnel deployed in Central Africa as part of its MINUSCA mission, one of the world body's largest peacekeeping forces.
The UN Security Council on Thursday voted to temporarily renew the mandate of the mission until December, amid heated debates about its ability to stem the unrest.