The incident occurred on Monday evening in the Derbent District, when police attempted to stop the man for a document check.
"On being ordered by police to stop and show his documents, the unidentified person shouted 'Allahu Akbar', opened fire, and attempted to escape. Police returned fire," a spokesman told RIA Novosti.
The man is believed to have been fatally injured by the grenade he threw at the officers, the spokesman said.
The man was found to be carrying an automatic rifle with a large amount of ammunition. He is considered a suspect in a recent attack on a local police post, in which three officers were injured.