The officer was identified late Monday as 51-year-old Officer Eric Talley, one of the first on the scene, American media reported on Tuesday.
The shooting was reported just after 11:40 p.m. in the 900 block of Box Elder Street south of downtown Pueblo. The area is residential.
A shirtless man with blood running down his leg was escorted out of the store in handcuffs by two police officers. A local hospital confirmed receiving one patient from the active shooting scene.
Officers were initially called to the King Soopers in the southern part of the city of Boulder for reports of a man shot in his vehicle, NewsNation affiliate KDVR-TV reported.
When officers arrived the suspect began shooting at them, police said.
Officers had their guns drawn, and some windows at the front of the store were broken. Authorities over a loudspeaker said the building was surrounded and that “you need to surrender.” They said to come out with hands up and unarmed.
Colorado Gov. Jared Polis issued a statement Monday on the events at the supermarket.
“Like my fellow Coloradans, I am closely watching unfolding events at King Soopers in Boulder. My prayers are with our fellow Coloradans in this time of sadness and grief as we learn more about the extent of the tragedy,” Polis said.