As previously reported, the invite - which featured the couple's faces inserted on the bodies of two farmers seated on a tractor - showed that the ceremony will take place on June 11 in Gloucestershire.
Writing on Twitter, Allen appeared to confirm that the leak is genuine and told whoever was behind it not to attend anymore.
"Oh and whoever leaked my wedding invite to the press, you're a d**k and your not invited anymore (sic)," she stated. "Have some respect and stay at home."
Allen and Cooper began dating in 2009 and became engaged on Christmas Day last year.
The 25-year-old is currently featuring in Channel 4 fly-on-the-wall series Lily Allen: From Riches to Rags.
> Lagerfeld 'to design Allen wedding dress'