Less than an hour after the attack, a second bomb in a car opposite the police station was detonated, wounding an investigator of the local prosecutor's office.
The two blasts damaged the police headquarters and nearby houses, and destroyed several cars.
Russia 'very tense'
The attack came as Russian authorities continued their hunt for those responsible for twin suicide attacks on the Moscow metro last week that killed 40 people.
The so-called Caucasus Emirate, an Islamist group led by Doku Umarov, a Chechen anti-government commander, has claimed responsibility for the metro attacks.
Those attacks were followed by suicide bombings in the Dagestan region of the North Caucasus that killed 12 people, including a local police chief, and a blast that derailed a cargo train.
Neave Barker, Al Jazeera's correspondent in Moscow, said the attack came at a time when Russia is "very tense indeed".
"Parallels have already been drawn between this latest attack ... and the attack that took place in Dagestan on Wednesday ... Clearly the response of this is one of deep concern," he said.
"There have been a number of attacks in recent months particularly in Ingushetia close to police stations and army barracks.
"The fear is that following last week's [attacks] that led to the deaths of at least 50 people, this spells an escalation of violence as a whole."
One of the two suicide bombers on the Moscow subway has been identified as the 17-year-old widow of a slain Islamic fighter from Dagestan.
Novaya Gazeta, a Russian newspaper, reported on Monday that the second Moscow suicide bomber may have been a 28-year-old schoolteacher from Dagestan.
The North Caucasus has been the site of two wars in Chechnya and hundreds of violent attacks since the 1991 collapse of the Soviet Union.
Violence has spread from Chechnya to the neighbouring regions of Dagestan and Ingushetia.