The incident with the car occurred near 14 Yaroslav Khomov Lane, about one kilometre (0.62 miles) from the Russian Embassy, the publication said.
Firefighters who arrived at the scene extinguished the fire.
The newspaper published the car's plate numbers — DP 001 019. It specified that the DP 001 plates belong to cars from the Russian diplomatic mission, consular offices, and members of the diplomatic staff.
The video of the incident has been published by the Ukrayinska Pravda.
The incident occurred after protesters gathered outside the Russian Embassy in the Ukrainian capital to protest against Russia's response to three Ukrainian vessels breaching Russian waters in the Kerch Strait earlier the same day.