According to Russia's TASS news agency, the car exploded near the village of Bolshiye Vyazemy in the Moscow region.
The car caught fire, lost control and flew to the other side of the road. Darya Dugina, born in 1992, died on the spot, Xinhua reported.
The car reportedly belonged to her father, a prominent philosopher and social activist.
Local law enforcement has started an investigation into the incident.