Sunday's attack (local time), in which 12 police were also wounded, hit the entrance to a concert hall in the Chechen capital, Grozny, where festivities had been planned to celebrate a local holiday, which was also the birthday of Chechen head Ramzan Kadyrov.
It was the first such attack in Grozny for two years and Kadyrov, 38, who is backed by Russian President Vladimir Putin, vowed to track down those behind the blast.
"We will search for these enemies of Islam everywhere and won't even allow their spirits to enter Chechnya. Severe punishment awaits those who helped carry out these murders," said Kadyrov on his Instagram account.
"No one should doubt. We paid a high price for peace in Chechnya and we won't allow illegitimate filth to shatter it," he said in the caption of a photograph of Muslim worshippers performing morning prayers.
Despite the relative calm in Chechnya after two separatist wars in Chechnya in 1994-96 and 1999-2000, the Islamist insurgency has spread across the predominantly Muslim North Caucasus, fuelled by a mixture of religious fervour and anger over corruption and alleged rights abuses.
The violence, which once targeted Russia's heartland, has increasingly focused on the North Caucasus itself where insurgents aim to carve out an Islamist state.
Kadyrov said the 19-year old suicide bomber, whom police said had left home two months ago, had dressed up as a police officer and detonated his explosive device when officers approached him asking for identification papers.
No group has said it was behind the bombing, but a video shown on Kavkaz Center, a website sympathetic to the insurgency, showed four bodies in pools of blood following the attack.
Analysts say resentment among North Caucasus residents has risen in recent months following harsher security measures to clamp down on suspected insurgents.
Human rights groups have implicated the Chechen authorities in the clampdown that has been accompanied by abductions and torture of suspected militants and their families.
"This is not a path to a long sustainable peace and could lead to new escalation from the militants," said Varvara Pakhomenko, an analyst on Russia's North Caucasus insurgency.
"Such harsh actions by law enforcement officials in (neighbouring) Dagestan and Chechnya are seen as unfair treatment of Muslims and may lead to a reaction against the authorities," she said by telephone.
Kadyrov calls the accusations an attempt to discredit his leadership and the peace he says he has brought to the region.
It was the first suicide attack carried out since the death of former insurgent leader Doku Umarov was announced early this year. The circumstances around his death, including when, where and how he was killed, are still murky.
Umarov's successor, Ali Abu Mukhammad, has urged supporters to refrain from carrying out attacks that would harm civilians.
