Parent-led group Scotstoun Woodies found out last week that they were being evicted from their base after 15 years.
The club used four rooms at Scotstoun Primary School to hold activities on Tuesday evenings.
But the organisation is likely to be one of many to be told to move on as Glasgow City Council looks to "cluster" school lets in a bid to save money.
They want to move groups from older schools into secondaries where there are other clubs using the facilities at the same time.
It is understood the Woodies, part of the UK-wide Woodcraft Folk group, was the only club in the school on Tuesday night, meaning the council had to pay for a janitor, as well as utility bills.
Parents at the group, which meets every Tuesday evening for around 50 children aged from five to 18, said they were shocked.
Stephen Lappin's 14-year-old daughter has been attending Scotstoun Woodies since she was five.
Mr Lappin, 49, from Scotstoun said: "There is concern among parents over this. We feel like we've been at the school forever.
"The primary school is seen as a hub of the community and it's a big change for us to be asked to move on.
"We have four sessions at different times on a Tuesday and have children as young as five at our club, so moving is going to put people out. It's a shock to us."
The group is currently using rooms at St Thomas Aquinas Secondary School.
The decision to go ahead with the "clustering of school lets" was made on February 7.
The council believes it will save £430,000 during 2013/14 but the move to limit access to some schools has raised concern among councillors.
Garscadden and Scotstounhill councillor Graeme Hendry said: "Yet again we see the leader of the council closing access to local primary schools when they should actually be at the heart of every community in Glasgow.
"We should be proud of the many community groups using our schools and not making things harder for them."
A spokeswoman from Glasgow City Council said: "Organisations still have access to school facilities, but our aim is to manage this in the most efficient and cost-effective way in the current financial climate, so as to protect frontline services.
"Scotstoun Woodies have been offered an alternative let close to Scotstoun Primary."