The inmate, aged under 40, was exposed to infected poultry while working at a processing plant in Montrose County as part of a work-release programme, state health authorities say.
He had recovered after experiencing mild symptoms including fatigue, and had been isolated from other prisoners and treated with the antiviral drug oseltamivir, they added.
No other cases have been detected, and Colorado officials say the risk to the public is low, as human-to-human transmission of the H5N1 avian flu is rare.
“We want to reassure Coloradans that the risk to them is low,” said Dr Rachel Herlihy, a state epidemiologist the Colorado Department of Public Health and Environment (CDPH).
The infected poultry had been “euthanised and disposed of,” the CDPH said.
While human infections of the H5 viruses are rare, direct exposure to infected birds increases the risk, the CDPH added.
It was only the second known case of bird flu in humans linked to a recent strain that was first detected in the United Kingom in January, and the first case in the United States, the US Centers for Disease Control and Prevention said.
Public health officials warned people should avoid contact with poultry that appear to be ill or are dead, and avoid contact with surfaces that appear to be contaminated with faeces from wild or domestic birds.
Climate experts have warned that global warming could increase the risk of outbreaks of infectious animal-to-human diseases.