Interfax quoted police as saying the car blew up near a village in western Dagestan and that a third person was in hospital with serious injuries.
"According to preliminary information, an explosive device transported in the car spontaneously went off," a police spokesman said.
On Wednesday, suicide bombers killed at least 12 people in the Dagestani town of Kizlyar, two days after deadly attacks in Moscow that authorities linked to insurgents from the region.
On Monday, Moscow was hit by its bloodiest attack in six years -- twin morning rush-hour blasts that killed 39 people. Authorities blamed female suicide bombers with connections to the mainly Muslim North Caucasus