Interior Minister Ihor Klymenko said special tactical police units stormed the store after attempts to contact the gunman with a negotiator failed.
The attacker was killed while resisting arrest, he said.
"The shooter in Kyiv was liquidated during the arrest," Klymenko said on the Telegram.
Speaking to reporters at the scene, Klymenko provided no speculation as to the assailant's motives but said that police negotiators spoke with the attacker for about 40 minutes.
"We tried to persuade him, knowing that there was likely a wounded person inside. We even offered to bring in tourniquets to stop the bleeding but he did not respond," Klymenko said.
"Consequently, the order was given to neutralise him."
Klymenko, who wore body armour, said the man was carrying a carbine, which was legally registered.
"Furthermore, in December of last year, 2025, he approached the licensing authorities to have the weapon test-fired as the permit was expiring. He provided a medical certificate. He had also submitted an application to renew his permit for the weapon. That is all we can say for now," Klymenko said.
He added that the investigation will determine which medical institution issued the certificate.
The shooting took place in Kyiv's Holosiivskyi district, Mayor Vitali Klitschko said.
Televised footage of the scene showed police taking cover in the shopping mall that housed the supermarket while shots were fired.
Bystanders were escorted away from the scene.
with AP