The blaze erupted around 1 p.m. (0900 GMT) at the Moscow State Institute of State and Corporate Management, said Viktor Beltsov, spokesman for the Emergency Situations Ministry.
He said at least four people were killed and 29 were treated for smoke inhalation, burns and other injuries.
Russia records nearly 18,000 fire deaths a year - several times the per capita rate of the United States and other Western countries.
Deadly blazes at schools, hospitals and other state-run facilities in recent years have revealed official negligence and rampant violations of fire safety rules.
The head of Russian Technologies, Sergei Chemezov, clarified the fate of anti-aircraft guided missiles that Russia was supposed to deliver to China
The Basmanny Court of Moscow arrested Michael Calvey, the founder of Baring Vostok investment fund, on allegations of embezzling 2.5 billion rubles from Vostochny Bank. Calvey will be held in custody until April 13