A Kildare school was forced to close yesterday after several students tested positive for Covid-19.
The HSE advised the school on Thursday that following a risk assessment, it was recommending that students and staff remain home as it investigates the outbreak.
"Following today's risk assessment we recommend that the school would close while the investigation is ongoing," the HSE said in a letter to the school principal.
"We will keep in regular contact with you as the results of further testing come through."
Social Democrats councillor Nuala Killeen said there had been several positive cases.
"Any student that develops symptoms is advised to contact their GP to seek a test. In the interim and in line with procedure all identified close contacts are advised to restrict their movements," she said.
"Wishing all the students and educators a speedy recovery."
Meanwhile, new figures show there have been 142 positive cases of Covid-19 in schools since they reopened, the HSE has confirmed.
More than 2,000 schoolchildren and teachers have been tested so far.
The confirmed cases are from 99 schools across the country.
Separately, concerns have been raised following reports that teachers who would be marked as close contacts by the HSE Covid Tracker app are now having that status removed and not being advised to isolate or seek testing.
Sinn Féin education spokesperson Donnchadh Ó Laoghaire has raised the issue with the Government and is awaiting a response.
"Teachers are just as susceptible to Covid-19 as any other user of the Covid Tracker app," he said.
"It cannot be that there is one rule for the public, and another rule for teachers.
"Surely, a close contact is a close contact, regardless of profession. It is completely unfair to have lower standards for school staff."
As Dublin enters lockdown this weekend, universities in the capital are to carry out most teaching online and suspend all on-campus club activities.
All universities have agreed to set measures, with students having limited access to college campuses. Some on-campus elements of orientation will still go ahead for first year students but will be staggered.
Libraries will remain open but will be subjected to social distancing protocols."