One of the victims suffered life-threatening injuries, doctors said.
Police spokeswoman Raquel Lopez said two men knocked on the door of an apartment Thursday night and sprayed the woman who answered with a flammable liquid and tossed a match or lighter at her. The men then entered the home and set two males and another female on fire, KMGH-TV, Denver, reported.
The woman who answered the door suffered the most serious injuries and was being treated at the University of Colorado Hospital, The Denver Post reported. The other three victims suffered comparatively minor injuries.
"This is something I've never seen in my years ... someone set someone afire like this," said Denver police spokesman Sonny Jackson, quoted by ABC News Radio. "This is highly unusual."
Police investigated whether the incident was related to an attempted robbery at a check-cashing service the same night 3 miles away.
Witnesses said they saw two men enter the establishment, spray flammable liquid on the counter inside the protective glass of the cashier enclosure, then light it.
The female employee on duty at the service was not injured, KMGH reported.