An unidentified woman blew herself up near a police checkpoint in the capital of Russia's North Caucasus region of Chechnya, Grozny.
Police said the bomber died in the November 17 blast but no one else was injured.
Acting Chechen police chief Apti Alaudinov told the RIA Novosti news agency that the woman's behavior made police suspicious.
When they asked her for identification, they noticed the explosive device and opened fire on her, he said.
Chechnya has been the scene of low-level unrest since Russia fought two wars against separatists in the 1990s and the early 2000s.
A state of emergency in the republic was lifted in 2009.