At least one person jumped to escape Monday night's blaze.
Injuries range from light to moderate.
Fire Capt. Allen Robnett said some people were hanging out windows when firefighters arrived and numerous people were rescued with ladders from the four-story building.
It's near the University of Colorado's Anschutz Medical Campus where some victims of last month's Aurora theater shooting were taken and where suspect James Holmes studied. It's also about a block away from Holmes' apartment.
Firefighters are investigating a witness report of someone with a gas can leaving the building but say there's nothing to indicate a connection with the shooting.