The victim, 44, got in the path of the approaching police car when he attempted to make an illegal U-turn on Novy Arbat, local news reports said.
The two officers in the Ford police cruiser suffered only minor cuts and bruises thanks to their car's airbags, Interfax reported.
The busy thoroughfare where the crash took place had been cleared of traffic for Putin's armored black Mercedes and its escorts, which sped by the crash site minutes later on their way to deliver the president to work in the Kremlin.
The victim, Lavrenty Gabrielyan, a resident of Mytishchi in the Moscow region, was talking on a mobile telephone while attempting to make the turn, according to Interfax.
"As the escort was moving past, the red Volkswagen was blocking the street and was hit by the first car in the escort and pushed onto the sidewalk," an eyewitness told Reuters. "The red Volkswagen's driver was apparently dead on the spot. He was covered with blood."
Television reports showed the victim's car, a Volkswagen Passat, with the driver's side crushed and its door sheared off.
The front of the police car was also smashed.
Quoting an unidentified high-ranking traffic police official, Interfax said the policemen in the motorcade did not deliberately strike the victim's car, as had been earlier reported.
The Kremlin immediately distanced itself from the crash, saying in a statement aired on television that the police car did not belong to the official presidential escort of Mercedes cars.
The president's motorcade is a constant source of irritation to Moscow drivers.
Police close off streets to traffic on the many days in which Putin travels to work in the Kremlin from his suburban residence.
Police cars then speed by ahead of the motorcade.
While shutting off streets for official motorcades is common in many countries, Russian drivers say it happens too frequently and for too long in Moscow, where numerous other VIPs get similar treatment.
The situation is made worse by the reckless driving of many Russian drivers and the fact that the capital's already traffic-clogged streets are becoming increasingly congested as more people buy cars.
Last summer, drivers complained about having to wait in traffic for hours under a scorching sun, after which the State Duma appealed to the Kremlin to cut down on its number of motorcades.
Police escorts have crashed into cars in the past, but this was the first incident in which anyone was reported to have been killed, news reports said.
Friday's crash is now under investigation, Interfax reported.
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