Unverified footage posted on Telegram appears to show Mr Dugin watching in shock as emergency services arrive at the scene of the burning wreck of a vehicle.
The BBC has not been able to verify the footage independently.
Investigators confirmed that Ms Dugina died at the scene near the village of Bolshiye Vyazemy.
They said an explosive device planted under the car went off and the vehicle caught fire. Forensic and explosive experts are investigating.
A Ukrainian official has dismissed accusations of Ukrainian involvement in the incident.
"Ukraine, of course, has nothing to do with this, because we are not a criminal state, which is the Russian Federation, and even less a terrorist state," said Mykhailo Podolyak, an adviser to President Volodymyr Zelensky.
Maria Zakharova, spokeswoman for Russia's foreign ministry, said in a Telegram post that if any Ukrainian link was found it would amount to "state terrorism".