About 50 people have been injured in the incident at the cinema complex in the suburb of Aurora.
Witnesses say a gunman wearing a gas mask opened fire during a midnight showing of The Dark Knight Rises.
A 24-year-old man was arrested in a car park nearby in possession of a rifle and hand-gun. He told police that explosives were stored at his home.
Police chief Dan Oates told reporters that an apartment block in the north of Aurora had been evacuated as a consequence of that information.
More weapons may have been left in the cinema, he said.
‘No terrorism link’
The incident at the Century 16 cinema complex began at approximately 00:30 local time (06:30 GMT).
“Witnesses tell us he released some sort of canister. They heard a hissing sound and some gas emerged and the gunman opened fire,” the police chief said.
“The shooting apparently went on for some time,” he said.
Ten people were killed at the cinema and four others died later at hospital of their wounds, he said.
The FBI, which is working with the police, say there is no terrorism link so far.
One witness said a man in a bullet-proof vest and riot helmet had been “slowly making his way up the stairs and just firing – picking random people”.
An eyewitness told the BBC that about 30 or 40 minutes into the film a man came into the right-hand exit nearest the front row.
“I’m pretty sure wearing [a] mask. He fired a canister into the air – it could have been a smoke bomb or tear gas,” the woman, identified only as Pam, told the BBC.
“It shot it right into the air, then I started to hear the bang, bang, bang of a gun.
“I crawled my way through the row, luckily the exit was close to where I was sitting so I got out pretty fast. I heard more shots as I left,” she said.
Another eyewitness, Salina Jordan, 19, told the Denver Post she had seen one girl shot in the cheek, and a girl who appeared to be about nine years old with a gunshot wound to the stomach.
A witness in the next-door theatre told 9News that when he heard loud bangs and a lot of smoke and initially thought they were live special effects put on by the cinema.
Projectiles came through the wall from the neighbouring screening, he said.