"It was a terrorist act," a duty officer at the regional prosecutors' office told Reuters news agency.
The officer said a police patrol had been sent to investigate reports that car packed with explosives was parked in the town's centre.
"When police approached the Lada, it blew up," he said. "There was virtually nothing left of the Lada car.
The bodies of three people, apparently policemen, could be seen on the ground before the area was cordoned off, and a fourth person was rushed from the scene in an ambulance.
According to the southern Russia branch of the Emergency Situations Ministry, three to five other people, apparently civilians, were injured.
A series of recent attacks against officials and police, blamed on Muslim fighters, has heightened security fears in Ingushetia. Earlier this month 2,500 troops were sent to the region to support local security forces.
Ingushetia, which borders Chechnya, is populated mainly by the Ingush ethnic group.
Earlier on Friday, armed men broke into a home in the province and killed three members of a Russian-speaking schoolteacher's family, officials said.
The shooting was the second such attack this summer and has increased fears amongst Russians in the region were being targeted, possibly in an effort to increase ethnic tensions.