Gunmen opened fire at Crocus City Concert hall near Moscow in 2024, killing 149 and injuring more than 500.
A traffic police officer and the suspect were killed in the explosion, Russian officials say.
Russia's economy is hanging between stagnation and decline, and ordinary Russians are beginning to feel the pinch.
The suspects include the alleged gunman, Lyubomir Korba, whom Russia says fled to the UAE after the attack.
Lt Gen Vladimir Alexeyev was shot several times inside his apartment block on Friday morning.
Lt Gen Vladimir Alexeyev is a senior figure in the main directorate of Russia's military general staff.
Russia editor Steve Rosenberg reports from the outskirts of the Russian capital, where Lt Gen Vladimir Alexeyev was shot and wounded.
The BBC's Russia editor speaks to people in the country as the war in Ukraine nears a fourth year.
A device was detonated after police approached a "suspicious" individual in Moscow, authorities said.
