Muravyov was born into the family of an officer of the Red Army on 2 October 1938 in the village of Dyatlovka [ru], Moscow Oblast, then part of the Russian SFSR, in the Soviet Union.

[1][2] He joined the Soviet Armed Forces in August 1955, and graduated from the Kharkov Higher Military Command-Engineering School [ru] in 1960.

[1] After carrying out further studies at the F. E. Dzerzhinsky Military Academy from 1973, and graduating with a gold medal in June 1975, Muravyov was appointed commander of the 306th Rocket Regiment.

[1][3] In November 1976 he became chief of staff and deputy commander of the 24th Guards Rocket Division, based at Gvardeysk, Kaliningrad Oblast.

[1] During his time in command, the 49th Guards Rocket Division was equipped with the RSD-10 Pioneer intermediate-range ballistic missile system, replacing the R-12 Dvina.

[2][4][5] In October 1979 the division was inspected by Colonel General Mikhail Grigoryevich Grigoryev [ru], the first deputy commander of the Strategic Missile Forces, and was rated as "good".

[4] His funeral was held at the Main Military Clinical Hospital [ru] in Moscow on 25 January 2020, followed by his interment in Troyekurovskoye Cemetery.