Chairman Adam Pearson confirmed the Dane's dismissal: "Unfortunately is has not worked out. Results have not been good enough and Jan has left the club.
"We will be appointing a new manager in the morning who will be in charge for our next game."
He added: "We need to turn it around."
Former Southend, Gillingham and Brighton manager Peter Taylor is expected to be named as Molby's successor. Taylor, who has also coached the England national side and the Under-21s, is currently without a club. He left Brighton at the end of last season after guiding them to the Division Two championship. Recently he has been helping out with coaching at Peterborough, but the Posh have confirmed that he has left that role.