Education Minister Leighton Andrews says a Carmarthenshire school staying open with no pupils is "bonkers".
He blamed the local council for Capel Iwan primary, near Newcastle Emlyn, staying open, even though its 12 pupils left in July.
He said: "If I had the powers, I would tell them to close it."
But the council said the school had had no warning pupils were not returning next term and it had to stick to Welsh Assembly Government procedures.
Capel Iwan school has been told by local education officials that it must be ready to open in the autumn.
Its £110,000 budget includes a head teacher, caretaker and dinner lady, as well as heating and lighting costs.
Carmarthenshire council said it was obliged to follow the assembly government's statutory consultation process before it could shut the school, a process that could take up to 12 months.
Mr Andrews put the blame for the situation squarely with the local authority, and told BBC Wales: "It's entirely the fault of the local council. They have known for some time that this school was losing numbers.
"As I understand it, the [consultation] process has not started yet. There is not a role for the assembly government unless the process starts.
"Why didn't they start the process about a year ago? Why didn't they start the process at the beginning of this year, when there were only 13 pupils on the register?
"The council has been lackadaisical. It's a complete failure of strategic leadership on the part of the council and a waste of money."
He added that it was time to "time to ask real questions about the structure and responsibilities of organisation in education in Wales"
He cited school inspection body Estyn as saying it had found "important shortcomings" in four of seven local education authorities it had inspected.
He said: "There are clearly problems in the system.
"It is not only the issue we see today of this school being kept open despite the face that it has no pupils, we see the different rates being paid for supply teachers in different-sized authorities around Wales.
"It's quite clear that some have got their act together, others haven't."
A Carmarthenshire council spokeswoman said the school's budget ran over the financial year, so some had already gone on costs incurred while pupils were attending.
The caretaker and dinner lady had been given notice and the head teacher would be working elsewhere within the education authority, she said.