The six-foot tall life-size figure, named PC Bobb, was placed in a Sainsbury's Local store to deter shoplifters.
The model was stolen last Saturday evening and photos of it have appeared on social networking sites, including appearing at several house parties since being stolen from the shop in Shafton, Barnsley.
A Sainsbury's spokesman said: It is bizarre that someone would want to steal our cardboard copper PC Bobb. We'd got used to having him being around and hope he is returned in one piece.
The props have been placed in the windows of stores around Barnsley as a crime prevention measure.
Forces had argued the cut-outs would boost public confidence, deter criminals and make the police more 'approachable'.
Greater Manchester Police claimed the presence of a cardboard policeman at an Asda story in Leigh had cut shoplifting by 75 per cent.
However in 2010 Essex Police abandoned a ã2000 scheme of 20 cardboard police officers dotted around after they were stolen.
Members of the public claimed they were a waste of funds and placed the public at risk of ridicule.
An Essex Police spokesman said: The trial of the cardboard police officers shows they had very little effect on crime or antisocial behaviour and we will not be continuing with their use.
