Russian television showed thick black smoke rising from inside the yellow four-storey building of the Central Research Institute of the Russian Air and Space Forces.
Several of the institute’s employees had to jump out of windows on the upper floors to escape the flames, according to witnesses quoted by broadcasters.
The Tver regional government said in a statement carried by state media that six people were killed and 21 injured in the blaze, updating earlier tolls.
Preliminary information suggests the fire was caused by faulty electric wiring, the TASS state news agency said.
The defence ministry said the institute focuses on research related to Russian air and space defence, as well as the development of new anti-aircraft systems.
Accidental fires are common in Russia, where hundreds of blazes are recorded each year due to ageing and dilapidated infrastructure and non-compliance with safety standards that are often lax.