The officer, Eric Talley, 51, had been with the department since 2010. Chief Maris Herold of the Boulder Police Department said Talley acted heroically as the first officer on the scene.
The suspect, who was injured, is in custody.
Herold said law enforcement would be working with the coroner's office over the next few hours to identify the victims.
"I know there are people out there waiting for an answer, and we will work around the clock to get this accomplished," she said.
Boulder District Attorney Michael Dougherty said a "painstaking investigation" was underway. He also noted that Colorado had seen numerous mass shootings in past years.
The Boulder Police Department first tweeted about an "active shooter" at a King Soopers grocery store at 2:49 p.m. MT. Following reports of the shooting, aerial coverage from the local news station KKTV revealed a large law-enforcement presence in the parking lot outside the grocery store and several medical helicopters hovering and landing near the scene.
The Boulder Police Department tweeted at about 4:20 p.m. MT that the area was still "very active." The department also sent a tweet urging residents to remain inside and avoid the area near the intersection of Table Mesa Drive and South Broadway, near where the shooting took place in in the southern part of the city.
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