Glasgow City Council has written to all parents who expected their children to start in P1 at Hillhead Primary School in August, telling them that the number of pupils enrolled is greater than the places available.
The letter from Morag Gunion, the council's head of curriculum, learning and teaching, says that, instead of automatic entry, places for catchment area children will be allocated under existing rules for placing requests.
That means priority will be given to children with a medical condition who require to attend the school, followed by families who have siblings at Hillhead, and then single parents. After that, places will be allocated on the basis of whether families have a safe walking route to a local primary school.
Parents have been given just a few days to make an alternative choice of primary in the event their child does not secure a place, with the council expecting forms to be returned by February 3.
However, the letter has caused anger and confusion among families who enrolled their children in November, but were unaware there was an issue with capacity until the letters arrived on Saturday.
One father, who asked not to be identified, told The Herald: "It is a disgrace. The council must have known there was an issue, but this was the first we have heard of it.
"We know the school is popular, but there has clearly been mismanagement by the council because they have obviously underestimated the number of children in the catchment area."
The situation has highlighted the growing problems of over-crowding at Hillhead Primary School, in Gibson Street, since it opened three years ago after a merger with other primaries.
The school was built with a capacity of 632 pupils, but currently has 649 and this is likely to rise to 678 by August this year.
In the past, the council has said the problem is a result of the popularity of the schools as well as rising population trends. It may also be because some parents who would otherwise have opted for private schools are choosing to send their children to a state primary because of the impact of the recession.
The Scottish Government's move to legislate to cap numbers of children in P1 classes at 25 has also restricted flexibility.
Opposition politicians argue the council's school rational-isation programme has under-estimated the number of places schools will need. They have also criticised the local authority's decision to increase numbers so rapidly by taking children who do not live in the catchment area, despite warnings over the impact on its facilities.
The school has already lost its dedicated art room and music room, which are now being used as classrooms and there are plans to convert its library into a classroom.
A letter to current parents at Hillhead from the parent council sent last week highlights a number of other issues, including insufficient toilet facilities, pressure on the dining room, the teaching of drama, music and art and playground restrictions.
It also warns that the lack of gym space means "from August 2014 it is not going to be possible to timetable the required two hours of physical education that each child is supposed to have".
The letter adds: "The school works extremely hard to get round these problems and still successfully delivers high quality education to the children.
"However, the space issues are becoming critical and action needs to be taken to ensure that solutions are found for the future."
A spokesman for the council stressed that all families living in the catchment area would be given priority before those living outside the catchment were considered.
He said: "This is a standard process that we have used in other parts of the city when schools have become very popular."
When Nikki and Stephen Wallace enrolled their eldest son, Harry, into Hillhead Primary School in November there was no indication that he might not get in.
Nikki, a 40-year-old speech and language therapist, asked about overcrowding at the time because she had heard the school was operating close to capacity, but was told she would get a place because she lived in the catchment area.
Now the couple have been left angry and confused after getting a letter on Saturday morning telling them they no longer had automatic entry and might miss out. "It came as a complete shock because, until this weekend, we were expecting Harry to go to Hillhead in August," she said.
"Something has gone badly wrong if the council has only just realised there is an issue with too many people applying.
"We are now in complete limbo and don't know what to do next. We both work and there is no time to go and visit the other schools before we have to make a decision on where Harry will go if he doesn't get in."
Stephen, 41, a construction manager, said the council had taken away the right of parents to make choices about their children's education. He said: "They have filled the school to capacity with placing requests in the last couple of years without waiting to see how many children there are in the area.
"The council website goes on about parental choice, but that has been taken away from us."