Following the announcement yesterday (16 February), the cheeky bookmaker attached a large sign to the club's gates, which reads: "Welcome to Jurassic Park."
"While Muirfield members bury their heads in the sand this time round, we thought we'd prod the beast with our Jurassic sign," Paddy Power said.
Muirfield has been accused of being "stuck in the dark ages" after a vote in May last year fell 10 short of admitting female members - a result that was condemned by SNP Leader Nicola Sturgeon, "and pretty much anyone else with a brain", Paddy Power said.
A spokesperson for the bookies said: "The decision last May to not admit female members was about as progressive as a Donald Trump policy, and unsurprisingly it's driven a wedge between stuffy members and the outside world."
The club swiftly removed the sign, which prompted Paddy Power to accuse the "party-poopers" of lacking a sense of humour.
"To be honest we were a bit scared when one of the dinosaurs stormed out to take our sign down but overall it was a roaring success," the company said.
The prank was pulled off alongside McFrank, the Scottish division of London-based PR firm Frank.
Last month the mischievous brand also superbly trolled Liverpool FC ahead of the club's home game against Premier League leaders Chelsea, which ended in a draw.
It put up a sign outside Liverpool's stadium that read: "Advance warning: This road will be closed from 21.45 hrs Tuesday 31/01/2017 for Liverpool FC's end of season party."
Having exited the FA Cup with a shock defeat against Wolverhampton Wanderers, Paddy Power was suggesting that by the time the game finished, Liverpool's hopes of a major trophy would also be effectively over.