Shaw, who spent 11 years at the club as a player, took the role in the summer but has been deemed surplus to requirements following a review by new boss Mark Robins.
Development director Steve Waggott said Robins had reviewed the management structure in the weeks following his appointment.
He told the club's official website: "Mark has worked with the current staff for several weeks but had told the board on his arrival that he would review the way things were organised and the shape of the structure.
"He felt that he needed a flatter management structure and within that there was no need for an assistant manager role.
"Richard was told yesterday (Monday 15), we wish him all the best for the future and thank him for his efforts during a testing time for the club."