It happened in Buyofwe in the province Laba, in the south of the country.
Radio Okapi said that the train caught fire after crashing into a ravine. According to reports, it was carrying flammable material.
The train was running between Lubumbashi, the second-largest city, and the town of Luena, 2,000km (1,200 miles) from the capital, Kinshasa.
The province's governor Richard Muyej told the BBC there had been an accident but he cound not confirm deaths.
