The Scottish Government is responsible for deciding how much councils can spend each year.
Local authority umbrella body COSLA has suggested Finance Secretary John Swinney introduce a "flat-cash" settlement for 2015/16, which would mean council spending would remain the same as in 2014/15.
But Mr Swinney has suggested a finance deal which would result in Glasgow getting £15million less.
Recently Mr Matheson revealed that if Glasgow had been allocated the same percentage of the cash available for Scottish local government as it received when the SNP came to power, it would have an extra £78m to spend on services.
He said: "What Mr Swinney is suggesting would be the final insult.We are already having to cope with a number of inflation pressures.
"We have an increasing population and more school children, so we need to employ more teachers.
"We have an aging population, so we need to provide more social work services.
"And if wages go up by 1% that costs us millions of pounds.
"What we are looking at now is abandoning the agreed flat cash settlement for each council and instead introducing a formula that would rob Glasgow of an additional £15m.
"We are being asked whether we support a cut of an additional £15m in Glasgow's budget and the answer is no.
"We are calling in the strongest possible terms for Mr Swinney to honour the flat cash budget for 2015/16.
"Although we think it is deeply flawed and is unfair to Glasgow, it is £15m better than the budget option he wants to introduce.
"This is the first test for Susan Aitken, the new leader of the city's SNP councillors.
"Will she stand up for Glasgow or will she allow the Scottish Government to rob us of an additional £15m?
"This shouldn't be a difficult decision for SNP councillors. It's a no brainer."
Ms Aitken said: "As SNP group leader, I will always stand up for the best deal for Glasgow, so of course I join councillor Matheson in welcoming the flat cash settlement.
"Unfortunately councillor Matheson has chosen to throw his toys out of the pram and walking away from COSLA.
"That will cost the city dear and the SNP can't support this petulant behaviour."