The two thieves abandoned the animal after being chased from the shop in Lozells Road, Birmingham, on February 22.
It has now been handed to the RSPCA.
West Midlands Force Response tweeted: "What the duck!!! Policing is a strange thing at times.
"This poor duck was left in a shop when the offenders for a shop theft made off having brought him with them.
"Quacking work by officers and he's on route with the rspca."
Twitter user Rob asked: "Who do you send the bill to?"
Dr Ypsilon wrote: "Wow. Crime has beaked."
Chris W posted: "It wasn't me Mallard."
Ray Fessey wrote: "The thieves thought it was a Robber Duck...."