The bookmaker has taken over the baggage hall in the arrivals area at Dublin Airport for the tongue-in-cheek campaign, which will run over the next two weeks on 42 illuminated posters.
Taking a playful shot at France striker Theirry Henry for his controversial handball last week in the World Cup qualifier against Ireland, Paddy Power's posters read: "Paddy Power welcomes you to Ireland... unless you're called Theirry."
Paddy Power said: "We're a nation still reeling from last week's controversial result in Paris so it's refreshing to be able poke some fun back Thierry's direction.
"It's a safe bet that he won't be travelling through Dublin Airport anytime time but if he does, our adverts will be waiting."
Following last Wednesday's match, digital agency Love Manchester also took a cheeky shot at Henry, spoofing French brand Le Coq Sportif by creating Le Coq un-Sportif t-shirts.