"The suicide bomber triggered his explosive device when he was stopped by policemen outside the Grozny concert hall at a security checkpoint," a senior city official, told the Reuters news agency.
Ramzan Kadyrov, the Kremlin-backed president, said that the suicide attack was an attempt to stop it from carrying out operations against Islamist fighters, who have been battling pro-Kremlin authorities and Russian security forces in the region for years.
"It is an attempt to make our forces pull back from the area where a special operation is being carried out, an attempt to make us stop working to destroy the rebels," he said.
"We will not stop until we have eliminated all the rebels who target peaceful citizens, the security forces, the military and members of religious orders."
Chechnya had become relatively stabilise after Kadyrov took power in 2007, leading Moscow to declare an end to military operations in the republic in April.
But since then there have been a number of bloody attacks.
Also Sunday, four suspected separatist fighters were found dead after an explosion in a car in the Nazran district of Ingushetia.
On Saturday, Officials said that at least eight suspected separatist fighters were killed by security forces in two separate incidents in Chechnya and Ingushetia.
Dmitry Medvedev, the Russian president, gave Kadyrov's Chechen forces free rein to operate against armed groups in the neighbouring republics of Dagestan and Ingushetia after Yunus-Bek Yevkurov, the Ingush leader, was badly injured in an assassination attempt on June 22.