Sarvarov, 56, was the head of the armed forces' operational training department, the committee added.
It said one theory being investigated was that the bomb was planted with the involvement of Ukrainian intelligence services. Ukraine has not commented.
Sarvarov died in hospital as a result of his injuries, the committee said, adding it had opened an investigation into murder and illegal trafficking of explosives.
Investigators have been sent to the scene, in a car park near an apartment block in the south of Russia's capital.
Images from the area show a badly damaged white car with the doors blown out, surrounded by other vehicles.
According to Russian media, Sarvarov previously took part in combat operations during the Ossetian-Ingush conflict and the Chechen wars in the 1990s and early 2000s, and also led operations in Syria between 2015-2016.
