A mangled, burnt-out carcass was all that remained of the police car at an intersection in Grozny’s usually bustling centre, a reporter from the Reuters news agency said.
A passenger minibus with shattered windows was seen nearby.
A series of attacks by Islamist fighters on security forces and local leaders over recent months has shattered several years of relative calm and raised questions about the Moscow’s control of the north Caucasus region.
Leaders from across the area warned Dmitry Medvedev, the Russian president, last month that they were struggling to contain the violence which they said had permeated all spheres of society.
Russia has fought two wars against Chechen separatists since the early 1990s.