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.
Russian Finance Minister Anton Siluanov announced a possible move that Russia can take in response to new US sanctions
When the bill was submitted to Congress on August 2, the reason for imposing the new sanctions on Russia was based on Russia's alleged interference in the US presidential election in 2016, but then something clicked
The Central Bank of Turkey announced measures to protect the financial market of Turkey against the background of the collapse of the Turkish lira and conflict of interests with the United States of America