Police say a search of the plane turned up no explosives, and the flight took off an hour late for its destination, Salt Lake City.
The incident occurred Saturday. Officials say the plane carrying 54 passengers and crew was on the ground when the alleged threat was made.
Forty-nine-year-old Sergei Berejnoi of Sandy, Utah, was arrested on suspicion of endangering public transportation. Formal charges could lead to up 12 years in prison along with a $750,000 fine, according to the Denver Post.
According to paper, he was still being held Sunday night in a Denver jail on $15,000 bail.
The newspaper spoke with a woman at Berejnoi's home who identified herself as his wife. She said she spoke briefly with her husband and was "too upset" to comment further.
SkyWest Airlines, which operated the flight, says the search delayed takeoff by about an hour.