Greater Manchester Police have confirmed that two wedding rings were also taken from the Scotsman's property, which is believed to have been broken into between May 20 and 26.
"I am due to get married in the near future and this is an awful thing to happen to us before the wedding," ITV News quotes McArthur as saying. "If anybody has any information as to where my property is and can help the police return it to me, I would be very grateful."
Detective Constable Kevin Telford added: "It is unlikely the offenders will keep hold of the medal and may try to sell it on.
"Obviously, it is unusual for such an item to come on the market so I would ask anyone who is offered the medal or who has any information as to where the items are, to contact police."
McArthur won the FA Cup with Wigan in 2013, beating Manchester City in the final at Wembley.