The blast on Monday was the latest violence in Grozny, which remains a shattered city some six years after Russian soldiers invaded the province seeking to end a separatist insurgency.
A 12-year-old boy and a woman were killed in the blast, said Ruslan Atsayev, a spokesman for the region's Interior Ministry. The wounded included a police officer in a passing patrol car, he said.
The Interfax news agency had earlier quoted Deputy Interior Minister Akhmed Dakayev as saying that the boy had been helping at a nearby gas station when the blast happened.
The explosion occurred at about 2.45pm, just metres from the entrance of a popular restaurant called Hollywood.
A reporter saw armed paramilitary officers and investigators standing around what little remained of the car: twisted and burning metal and bent tyres. The restaurant's entrance was destroyed and its windows blown out. The blast shattered car windows.
The explosion occurred some 200m from a heavily protected compound of government buildings.
Regional President Alu Alkhanov was conducting a meeting in the compound at the time, state-run Vesti television reported.
The car bomb came a day after four Russian soldiers and a top regional officer were killed by a landmine in a region south of Grozny as they were trying to help a local administrator whose home was attacked by rebels.
Russian soldiers re-entered Chechnya in 1999, three years after withdrawing at the end of a disastrous 20-month war with separatist forces that left the province de facto independent.
Although the federal forces and allied paramilitaries control most of the small territory, rebels based in mountain hideouts mount regular hit-and-run attacks.
Violence has been spreading to
areas around Chechnya
Separately, a landmine exploded in the neighbouring Ingushetia province, west of Chechnya, seriously wounding a police chief and his driver, officials said. The landmine was detonated remotely as the car was passing.
The police chief was identified as Dzhabrail Kostoyev, of Ingushetia's main city, Nazran, said Roman Shchekotin, a spokesman for the federal Interior Ministry's branch in southern Russia.
Frequent attacks on police and the authorities in the regions surrounding Chechnya have raised fears that violence is spreading from war-torn Chechnya. Some of the violence is believed to be tied to criminal gangs.