Kroger said three employees were among those killed in the shooting at King Soopers in Boulder, Colorado.
They were Denny Stong, Rikki Olds, and Teri Leiker, the company said in a statement.
"In the hours since the shooting, we’re learning of truly heroic acts that included associates, customers, and first responders selflessly acting to protect and save others. We will remain forever grateful to the first responders who so bravely to protect our associates and customers," Kroger said, adding that the company was "horrified and heartbroken over the senseless violence."
"The entire Kroger family offers our thoughts, prayers and support to those impacted by this tragedy, including our associates, customers and first responders, and their families."