The Chaffee County Search and Rescue team said the unnamed man got lost and found himself without phone signal after being left by colleagues who went ahead without him.
He endured stormy weather and multiple falls before being found in a large search effort the next morning. He was stabilised and taken to hospital, but there has been no further update on his condition.
The officials suggested the incident “might cause some awkward encounters at the office in the coming days and weeks”.
The drama unfolded on Friday as a 15-strong group from the company – which has also not been named – ventured along a trail up Mt Shavano, which is 14,000ft high.
In their statement, officials said the hiker reached the summit on his own at about 11:30 local time, 17:30 GMT, but became disorientated on his descent.
His colleagues are said to have told him that he was on the wrong route, and suggested that he regain the trail.
But their teammate became still more lost after a strong storm passed by, bringing “high winds and freezing rain” and leaving him without phone signal.
Chaffee County Search and Rescue received an alert at 21:00 that evening, dispatching two teams and a drone pilot who were thwarted by the bad weather.
A helicopter was also sent, but despite tracing the man’s last known movements, the rescuers could not find him. He was wearing dark clothing.
Extra help was summoned from multiple agencies in neighbouring areas on Saturday morning, resulting in what the officials called a “large search effort”.
Eventually, the missing man recovered enough phone signal to make an emergency call, and he was located in a gully.
He reported that he had fallen at least 20 times and was left unable to get up. His rescue ultimately involved technical rope lowers and phenomenal cooperation and teamwork, the officials added.
The man’s health remains unknown after being taken for hospital care.