Shawn Pomrenke -- who is the co-owner of the biggest gold dredge on the show -- was arrested on December 9th in Nome, Alaska and subsequently booked on four counts ... DUI, failing to return to the scene of an accident, driving without insurance, and assault in the third degree.

According to the criminal complaint, obtained by TMZ, Shawn was backing out of a parking lot when he struck a pedestrian who was carrying groceries -- then took off ... "smiling and giving a thumbs up."

Cops caught up with Shawn down the road -- and claim the guy admitted to having a couple drinks ... and not having car insurance. According to police, Shawn then registered a blood alcohol level of .125 on a breathalyzer -- nearly twice the legal limit -- and bombed a field sobriety test.