It was the first suicide attack in Grozny in more than a year.
Kadyrov pledged that the police officers who sought to prevent the blast would be rewarded.
"It is unknown what [the bomber] wanted, it is on his conscience, while the police acted worthily," Kadyrov was quoted by the Interfax news agency as saying.
Chechnya has been the site of two brutal wars following the 1991 collapse of the Soviet Union.
Tens of thousands of people died in the conflicts between separatists and Russian forces, which has now deteriorated into small-scale skirmishes and hit-and-run attacks on police and government officials.
Violence has spread from Chechnya to the neighbouring regions of Dagestan and Ingushetia.