The Gavin Glynn Foundation says a number of families with cancer patients have contacted the foundation stressed and concerned over chemotherapy sessions being cancelled at CHI at Crumlin.
John Glynn from the children's cancer charity said: "The bed capacity in the actual children's hospital itself happens all year round and that it's not just a seasonal thing."
He said: "Cancer can't wait, you know the children can't wait for the new children's hospital to be built, something needs to be done now especially for all the children being diagnosed now and being treated with cancer.
"The numbers are increasing rapidly and these children need to have their treatment on the schedule that they've been put on for their clinical trials."
Mr Glynn added: "They need to have their treatment on that time and not be delayed because of lack of resources or lack of beds, it's just not acceptable."
In a statement, the hospital said the postponements were regrettable and said it was very cognisant of the impact it had on patients with cancer and their families.
The hospital said five patients were affected in December and all have since received the necessary treatment.
Three patients had their chemotherapy delayed by one day and two had to wait two days before receiving treatment.
The hospital said the decision to postpone the treatments was not taken lightly.
It said it was due to an increase in numbers attending the emergency department with flu and the winter vomiting bug.
Speaking on RTÉ's Marian Finucane Show, hosted by Brendan O'Connor, Taoiseach Leo Varadkar said: "this crisis is happening because of a failure to build the new national children's hospital a long time ago.
"It is wrong, it is terrible. What do we do about it? We build a new hospital"
Mr Varadkar said while the new children's hospital is not the answer to every issue in paediatric health, it should have been built a long time ago.
"Everyone knows hospitals get busier during the winter periods."
He said there are viruses and hospitals full of children with infection.
Mr Varadkar added when you have a hospital full of children with infection it is not a good idea to bring children in for their treatment as they risk infection.