Police used surveillance video to identify the suspect as 47-year-old Scott Ostrem. Television footage showed officers taking him into custody about 5 miles (8 kilometers) away from the Walmart after pulling over his car.
The shooting appears random and there are no indications that it was an act of terror, Thornton police spokesman Victor Avila said Wednesday night.
The motive was unknown, Avila said.
Two men died inside the Walmart, which is about 10 miles (16 kilometers) north of Denver in a busy shopping center. The woman died later at a hospital.
Authorities did not immediately release any other information about the victims.
Aaron Stephens, 44, was in the self-checkout line when he heard a single shot followed by two more bursts of gunfire before people started running for the exits.
"The employees started screaming. Customers were screaming. They were running like crazy, and I ran out too because I didn't want to get killed," he said.
Guadalupe Perez was inside the store with her young son when she heard what she thought was a balloon popping. A Walmart employee told her someone was shooting, and then Perez saw people running away yelling, "Let's go. Let's go. Leave the groceries."
"You see all these things in the news and you go through it, it's scary," she said. "But thank God we're OK and nothing happened to us."
Investigators, including special agents with the Bureau of Alcohol, Tobacco, Firearms and Explosives, were reviewing security video and interviewing witnesses.
Ragan Dickens, a Walmart spokesman, said the company is working with investigators.