After the attack in the village of Novoselitskoye in the southern Stavropol region, regional authorities ordered the tightening of security measures in kindergartens, schools and hospitals.
Russia's North Caucasus -- including Chechnya where the Kremlin has fought two wars against separatists over the past 20 years -- has been gripped by nearly daily violence for years due to a simmering Islamist insurgency there.
Attacks in the Stavropol region -- which is close to the Muslim-majority Northern Caucasus -- are rare, however.
"We were holding a meeting in the morning when five explosions went off," Sergei Karamyshev, a senior local police official, told AFP.
"Three people blew themselves up after an officer on duty at the entrance blocked the door to the building," said Karamyshev.
He said three of the explosions were caused by the suicide bombers, while a fourth was caused by a grenade.
The source of the fifth blast was not immediately clear, he added.
There was no immediate information on the identities of the bombers.
"There are only fragments of flesh over there," said Karamyshev.
A regional police spokeswoman said however that just one of the attackers had detonated an explosive charge while the other two assailants were killed by "return fire."
"They were shooting at the building," Natalya Tyncherova told AFP.
The lifenews.ru news outlet known for its close ties to police and security agencies posted an eyewitness video shot after the attack showing the police station with an alarm sounding and what appear to be fragments of bodies outside.
"There were five explosions and a volley of automatic gunfire," a male witness can be heard saying in the video. "There's no one here, everyone has run away in a panic."
Investigators said in a statement that "three unknown men" tried to storm the police station and detonated grenades, adding that the building and nearby cars had been damaged.
- 'Terrorist attack?' - In a sign of the significance of the incident, deputy chairman of the Moscow-based Investigative Committee which probes major crimes, Boris Karnaukhov, arrived at the scene.
President Vladimir Putin's spokesman Dmitry Peskov said efforts were under way "to understand what was behind" the attack, which is likely to be seen as a blow to the Kremlin's prestige.