The sinking happened on Monday after the boat's motor exploded, starting a fire that quickly engulfed the vessel, with terrified passengers jumping overboard, officials told AFP.
It had been carrying an estimated 100 people down the Oubangui River from the capital Bangui when the fire broke out near the village of Modale.
A naval official said at least 80 people were on board the New Jerusalem when it left Bangui, 125 kilometres (77 miles) upstream from where it came to grief. "But others had probably been taken on during the voyage bringing the number of passengers to more than 100."
Joseph Tagbale, the mayor of the port district of Bangui, said it was difficult to estimate how many lives had been lost. "We are asking the authorities to search to see if there are any survivors."
Overloaded and badly-maintained boats often sink on the Oubangui, with safety regulations rarely followed in the impoverished country, where thousands have died in fighting since a March 2013 coup.