Garrett Swasey, who was killed, was a campus police officer for the University of Colorado at Colorado Springs (UCCS)
Nine other people were injured during the standoff at the Planned Parenthood clinic, which lasted five hours before the suspect surrendered.
A number of people were trapped inside the building as shots were exchanged.
The motive remains unclear. The Planned Parenthood group has drawn anti-abortion protests in the past.
A law enforcement source identified the suspect as Robert Lewis Dear, from North Carolina. No other details were given.
“I want to convey to the loved ones of the victims, this is a terrible, terrible tragedy that occurred here in Colorado Springs today,” Mayor John Suthers told a news conference.
“Obviously, we lost two civilian victims. We mourn the loss of a very brave police officer.”
The dead policeman was named as Garrett Swasey, 44, who was married with two children.
Colorado Springs Police Chief Peter Carey said five police officers were among the injured, who were being treated in local hospitals.
Police had sealed off streets around the centre as officers tried to make contact with the suspect.
“We did get officers inside the building,” police Lt Catherine Buckley said.
“They were able to shout to the suspect and make communication with him and at that point they were able to get him to surrender and he was taken into custody.”
Police said the suspect had been seen carrying “some bags” into the building and teams were combing the area for possible explosives.
The suspect’s car which was found nearby was also being checked for explosives, CNN reported.
The manager of a nearby hair salon, Denise Speller, said she had heard as many as 20 gunshots in under five minutes.
She told a local newspaper she had seen one of two police officers appear to fall to the ground and the other attempt to get the wounded officer behind their police vehicle.
Police had told shoppers at a nearby centre to stay indoors.
In a statement, Planned Parenthood said it was not yet clear “if Planned Parenthood was in fact the target of this attack”.
“Our concern is for the safety of our patients, staff and law enforcement,” said its CEO, Vicki Cowart.
New York’s city police said it had deployed critical response vehicles to Planned Parenthood sites in the city because of the Colorado incident, but said there was no threat in the city.
Planned Parenthood is a healthcare non-profit-making group with 59 affiliates and 700 clinics around the US, some of which provide abortion services.