Ruslan Alkhanov, the Chechen interior minister, said the suicide bomber had been identified as a local resident.
An investigative committee of Russian prosecutors said two civilians had also been wounded in the attack.
Call for killing
A pro-rebel website, Kavkazcenter.com, quoted sources as saying the attack had been claimed by the Caucasus Emirate, a group said to be led by Doku Umarov, a Chechen separatist fighter, but the claim has not been verified.
The website also called for Ahmed Zakayev, a prominent separatist leader based in London, to be killed, saying he had abandoned Islam by recognising the legitimacy of Chechnya's Kremlin-backed government.
"Public remarks show that he [Zakayev] has fallen away from Islam. The court has ruled that the killing of this apostate is a duty for Muslims," the website said, but did not specify which court had ordered the ruling.
Zakayev, 50, fought Russia as a senior rebel commander in two wars with Moscow in 1994-2000.
After Russia regained control of Chechnya, he fled to Europe and acted as an official rebel envoy until 2007.
Russia has tried to extradite Zakayev for 13 alleged crimes including kidnapping and murder, but a British court rejected the request in 2003, causing a diplomatic row.
In recent months Zakayev has entered talks with representatives of the pro-Moscow government of Chechnya, led by Ramzan Kadyrov.
Last month Kadyrov said he would welcome Zakayev's return and possibly offer him a job in the regional culture ministry.
Rise in violence
The latest developments come days after four policemen were killed in two suicide attacks in Grozny, Chechnya's capital, and after a bombing in neighbouring Ingushetia killed at least 20 people.
Vladimir Putin, the Russian prime minister, flew into Chechnya on Monday to show support for Kadyrov, amid growing violence.
Chechnya has been ravaged by two separatist wars in the 1990s, following the collapse of the Soviet Union.
Although the conflict in Chechnya has ended, the Russian Caucasus remain the site of a deadly uprising led by fighters battling pro-Kremlin local authorities, who in turn have been accused of human rights abuses.