Nearly 170 were hospitalised, the officials were quoted as saying by the ITAR-TASS news agency on Monday. Many suffered broken limbs and one Ecuadorean student reportedly died after jumping out of the five-storey building to escape the raging inferno.
A criminal inquiry was launched and investigations were still going on to determine the causes of the fire, which could have been started deliberately, officials said initially.
With freezing temperatures outside, many of the students sustained injuries jumping from windows to escape the blaze in the five-storey concrete block housing students from the developing world at Moscow's Patrice Lumumba People's Friendship University.
Jumping from windows
"It happened very fast," said Richard Mallobe, a sociology student from Liberia. "Some people jumped and were burnt so we tried to get them into ambulances."
"I've never seen anything like this"
"People were jumping from the windows because it started on the second floor and there was no other way out. It was absolutely horrible," he said.
Among the casualties were students from China, Bangladesh, Vietnam and a number of African countries, the trade union of foreign students said.
Silvio Fernandez, 24, a language student from Cape Verde living in the block, said the blaze began at about 0200 (23:00 GMT) in two rooms on the second floor and spread to the rest of the building.
"After two hours, I could see people in the windows of the fifth floor leaning out and shouting," said Fernandez, who escaped by climbing down a ladder. "I've never seen anything like this."
Fire crews worked through heavy snow to control the blaze, which gutted the top three floors of the building. They extinguished the fire by about 0530 (02:30 GMT), the police spokesman said.
Moscow mayor Yuri Luzhkov said he suspected the fire was caused by an electrical fault.
"It is difficult to talk about the cause," he said. "According to preliminary information, the cause was domestic. Most likely, there was a short circuit in room 203."
However, Russian agencies reported a criminal investigation had been opened and authorities were not ruling out arson.
The Peoples' Friendship University, formerly known as Patrice Lumumba University, was set up in 1960 to train students from developing countries.