The publication ran a story that detailed the band's frontman Shaun Ryder being headhunted by David Cameron to help ease the government's recent 'pastygate' scandal.
The joke included Ryder allegedly bringing in various celebrities including David Walliams, Amy Childs, David Tennant and Miranda Hart to launch a T-shirt campaign titled 'We're All Eating This Together'.
Ryder was 'quoted' as saying: "I never thought I'd see the day when the prime minister was ringing me for advice. But let's face it, after the past week or so, with pastygate and everything, they obviously need help.
"People assume I'm a lefty because I'm working class and from Salford, but I'm not really. The Mondays were all children of Thatcher's generation. The hefty wedge they offered helped as well. It's funny because it seems like everyone else is paying for an invite to No 10 these days, and I'm the only one who is getting paid to go there, which is nice."
The Happy Mondays later denied the reports on Twitter, stating: "Shaun may be a Tory ..thats his choice..me n Paul are firm Labour....and if Cameron does come to a Mondays gig..we wont be greeting him (sic)."
Former X Factor contestant and Happy Mondays collaborator Rowetta Satchell later told them of the joke, saying: "Of course. April Fool from The Guardian!", prompting the group to reply: "is it? I hope so.."
The band later realised their error, writing: "April fool..ffs..how old are they..people still do that as adults...f*ckinell..the cold winter evenings must fly by."
The Happy Mondays are due to embark on an 11-date UK tour in May, but the group's member Bez recently pulled out of their plans.
Other April Fool's jokes this year include Google 'launching' an 8-bit version of Google Maps for the Nintendo Entertainment System.
> Shaun Ryder: 'Absolutely no plans for new Happy Mondays album'