The Investigative Committee branch for the Moscow region said the Saturday night blast was caused by a bomb planted in the SUV driven by Daria Dugina.
The 29-year-old was the daughter of Alexander Dugin, a prominent proponent of the “Russian world” concept ideology and a vehement supporter of Russia’s sending of troops into Ukraine.
Ms Dugina expressed similar views and had appeared as a commentator on the nationalist TV channel Tsargrad.
Using the familiar form of her name, Tsargrad said on Sunday: “Dasha, like her father, has always been at the forefront of confrontation with the West.”
The explosion took place as Ms Dugina was returning from a cultural festival she had attended with her father.
Some Russian media reports cited witnesses as saying the vehicle belonged to her father and that he had decided at the last minute to travel in another car.
No suspects were immediately identified.
Denis Pushilin, president of the separatist Donetsk People’s Republic that is a focus of Russia’s fighting in Ukraine, blamed it on “terrorists of the Ukrainian regime, trying to kill Alexander Dugin”.