The Salt Lake Tribune reports the fire had burned about half a square mile as of Monday afternoon.
Monument spokesman Dan Johnson says the most active area of the fire is on the north side of the monument and is burning in a steep canyon full of timber.
He says the perimeter of the fire extends into Jensen and Colorado.
He says crews closed the Canyon Overlook to use it as a base for fire operations, but no structures have been threatened and no campers have been evacuated.