The city council – which has one of Scotland's worst records for recycling – had hoped to keep its Cathkin landfill open for another two years.
But authorities in neighbouring South Lanarkshire – home to the site – have issued an enforcement notice demanding all operations end at the dump by mid-summer.
Council bosses in Glasgow are expected to appeal against the order from their neighbouring Labour council.
But the city has effectively been found to be illegally dumping at a site South Lanarkshire believes should have closed by August 2012 and its politicians are opposed to any attempt to appeal against the enforcement action.
East Kilbride Conservative Graham Simpson said: "Just for once Glasgow should do the right thing: pack up and go away and dump their rubbish somewhere else."
East Kilbride Labour Councillor Janice McGinlay said: "An appeal against this decision would be a slap in the face for local people."
Rutherglen LibDem Councillor Robert Brown added: "This really is a straight-forward matter of planning law and Glasgow should respect the decision of South Lanarkshire."
Glasgow's initial bid to open the landfill at Cathkin was knocked back in the 1990s by South Lanarkshire planners and only got the go-ahead after the former Scottish Executive backed city over shire.
Ever since problems – including scores of complaints about everything from flies to smells – have soured relations.
South Lanarkshire Council expected the landfill to close by August 2012 under the terms of initial planning permission, but Glasgow made a new planning application to continue to use the site which was unanimously refused last month by South Lanarkshire's planning committee.
Now that council has used its statutory powers to order Glasgow to shut a landfill that it is effectively operating in breach of planning rules.
A Glasgow City Council city spokesman said :"Glasgow is currently transforming the way it deals with waste and the city's use of landfill will decrease dramatically as new recycling and renewable energy facilities come on line.
"In the meantime, the city still requires some capacity and has been investigating options including extending the operating life, but not the size, of its existing site at Cathkin.