The Lada car, which contained a driver and three passengers, exploded at around 8:55 a.m. (05:55 GMT) on Tuesday some 50 meters from the Udelnaya metro station, in the city's north.
"When the car reached the metro station, the blast went off. A grenade exploded," the source said.
The source added that according to preliminary information, the grenade belonged to one of the passengers. He meanwhile ruled out the possibility that the blast was a terrorist attack, saying: "The version of this being a terrorist attack is unlikely."
Two passengers, including a child believed to be 2.5-3 years old, were killed at the scene, and another woman, who was among those injured in the explosion, died later. The driver has been hospitalized in a critical condition, police said.
The source added that the blast had not damaged the metro and had not affected operations.
A criminal case has been opened, and an investigation is underway.
