Lieutenant General Fanil Sarvarov, who led a special training unit within the Russian military, was the driver of the car that exploded and died shortly afterwards of his injuries, according to media reports.
The explosive device was reportedly attached to his car.
An investigation has been launched, Russia's Federal Investigative Committee (Sledkom) announced. The committee investigates serious crimes.
Several different leads are being investigated in the murder investigation. One of them is that the crime was carried out by Ukraine's intelligence service, said committee spokeswoman Svetlana Petrenko, according to the AP.
Since Russia attacked Ukraine, several deadly attacks have been carried out against Kremlin loyalists and high-ranking military personnel, both within Russia and in Ukrainian areas controlled by Russia.
Suspicions have been directed primarily at the Ukrainian intelligence service, which in at least one case has claimed responsibility, AFP notes.
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