The HSE has said that around 14,000 children are out of school and restricting their movements, as a result of being identified as a close contact of a confirmed case.
It is an increase of about 2,000 on yesterday.
As of this evening, 809 primary schools and 520 secondary schools have reported a Covid-19 cases. Yesterday the figure was 700 primary schools and 500 secondary schools.
The HSE has said it believes that the majority of Covid-19 cases are as a result of community transmission and not in-school transmission.
Each primary school case has on average 15 close contacts, while in secondary schools the figure is lower at around 4.
The Minister for Health acknowledged that the requirement for school children to restrict their movements for at least ten days, if they are designated a close contact of a Covid-19 case, is "a big imposition".
Stephen Donnelly said "we are seeing a large number of students having to self-isolate because they have been deemed to be close contacts and they of course will get tested" but he said it shows "the system is working".
"We are seeing students coming back into school, from the summer holidays, who will have contracted Covid in a community setting."
He said those people are being identified, which he described as very positive, and he said "the other thing that is very positive is that the public health teams are working really well with the schools to do the close contact tracing and indeed we had a very high number of tests yesterday."
Mr Donnelly said while the number of referrals for tests is up, and a lot of people are having to self-isolate, the positivity rate is falling among the younger age cohorts.
However he said "there will be some concern for parents. Obviously nobody wants their child out of school for five days, for ten days or whatever it maybe, but it's important that we got the schools back open again."
He said he wants to see a continued reduction in cases, which would make "incidents like this less and less frequent."
Asked about the knock-on impact of children having to restrict their movements for ten days, the Minister said "there is quite a long period right now in terms of the time the students have to be taken out of schools."
For those aged 12 years and over, Mr Donnelly said the requirements only apply to people who are unvaccinated.
"Nonetheless, it is a big imposition on the children and obviously on their parents as well. The public health teams can always keep the testing protocols under review and if they were to advise me and to advise government on shortening them, that's something we can look at. But what we are doing is implementing the current protocols."
The Irish National Teachers Organisation has described the figures on students out of school as "concerning."
In a statement the INTO said "we will be looking closely at the weekly report on schools mass testing in advance of our engagement with the Department of Education and public health officials" this week.
"The public health figures being reported are concerning."
It added that "it is vital that school communities continue to be aware that the coronavirus symptoms have been expanded this year and if in doubt, children or staff members with common or uncommon symptoms, should stay home from school and seek medical advice".
The Irish SME Association has said it is concerned about the knock-on impacts of children being required to restrict their movements for a lengthy period, which the employers body said could "very negatively impact both employers and their employees."
ISME chief executive Neil McDonnell said "when we are looking at a return to office working from 20 September, sending large numbers of children home is simply not going to be a tenable prospect".
He said ISME believes "one of the ways through it is going to be the provision of antigen testing".
He said "there can't be a requirement to keep perfectly fit and healthy children in a house for 10 days, when they can be given an antigen test which will tell within 15 minutes whether they are infectious or not, and that should be provided for ASAP".
Mr McDonnell said: "If we now over the next three weeks revert to a scenario where children are effectively being sequestered at home for two working weeks, awaiting a PCR test, that is going to very negatively impact both employers and their employees. And there is time it fix it now before 20 September, so we would urge Government to get on with it."
It had been due back from summer recess next Monday 13 September, but will now sit this Thursday to debate the approach to Covid cases in schools.
A number of schools have reported significant problems with absences amidst pressure on Covid testing, following a change in guidance from the public health agency.
Delayed care 'set to be major issue'
Mr Donnelly said that delayed care is set to be a major issue for the health service, with many of those who have delayed seeking medical care due to the pandemic becoming sicker and older as they enter into the health services.
The minister said that delayed cancer care and the deferred identification of cancer is a real issue.
Minsiter Donnelly said there were very ambitious plans for healthcare and a lot of extra capacity has been put in place in the last year, with the "mission" being to provide universal healthcare.
He said that the roll out of free contraception for women will begin next year as part of plans to improve women's healthcare.
He said that this year's winter plan is being put in place and will build on last year's "really successful…but very expensive" plan.
The minister said that last year's winter plan resulted in the lowest trolley numbers on record for the winter, but only a 12% in reduction in presentations at emergency departments.
Additional reporting Fergal Bowers