Wigan Athletic player James McArthur, who was born in Glasgow, spoke of his "devastation" after the memento from his side's victory over Manchester City at Wembley in 2013 was taken.
Two wedding rings were also stolen - shortly before the Scottish international is due to get married.
The 26-year-old said: "I am devastated, as is my fiancee. The medal is priceless for me and this is a real blow to us to happen just before the wedding.
"I am due to get married in the near future and this is an awful thing to happen to us before the wedding."
Mr McArthur said the culprits "ripped through" the house in Wigan and "took virtually everything of value".
He added: "It is very upsetting. 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."
Greater Manchester Police said the break-in happened some time between Tuesday May 20 and Bank Holiday Monday, May 26.
They have not specified whether they believe the burglary was carried out by a group or single perpetrator.
Detective Constable Kevin Telford said: "Understandably, Mr McArthur and his family are devastated someone has broken into their private property and stolen their possessions.
"Not only has an FA Cup medal been stolen but two rings that were going to be used in Mr McArthur's wedding have been taken.
"They are of huge sentimental value to them and while the rings can be replaced, the medal is something that cannot."
He said it was unlikely the burglars will keep hold of the medal and may try to sell it on.
Mr Telford added: "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."
Wigan Athletic claimed the first major trophy in their history when Ben Watson scored a last-minute goal to hand them a shock win over Manchester City at Wembley in May last year.