There has been a serious Covid-19 outbreak in Ballincurrig Care Centre, a nursing home near Midleton in Co Cork.
A small number of residents have been hospitalised due to Covid-related complications, but the majority of residents who tested positive are being cared for onsite.
Other residents who tested negative have left the home.
It is understood the HSE is giving a high level of support to the centre, as well as help with regards to staffing.
While the HSE said it would not comment on individual cases, it did confirm there were a "significant number of residential centres in crisis".
The HSE is also calling for suitably qualified people to volunteer as healthcare assistants and/or nurses, to help battle these outbreaks.
In a statement, the HSE said: "Cork Kerry Community Healthcare is supporting the residents of a significant number of private nursing homes where there are Covid-19 outbreaks, as well as supporting our own residential facilities where there are outbreaks.
"At present, there are more than 60 outbreaks in residential settings across Cork and Kerry (this includes nursing homes, community hospitals, disability centres and mental health services)."
The HSE said the majority of these outbreaks are in residential centres for older people, and the number of staff who are ill or on leave due to Covid-19 is presenting serious challenges.
"We would like to thank the many nurses and healthcare staff who have so far come forward to work additional hours and shifts, or who have been redeployed, and who are making such a difference at this time.
"We have requested the assistance of the Defence Forces in providing support around cleaning and waste disposal at a number of nursing homes in crisis, allowing our nurses and healthcare assistants to focus on the care of residents and patients."
However, more staff is still urgently required, particularly nurses and healthcare assistants.
Any nurses and healthcare assistants who are available and are not currently involved in direct care of patients or residents can contact chief officer Michael Fitzgerald on MichaelM.Fitzgerald@hse.ie.
"Finally, the best way for everyone else to support the efforts of healthcare workers is to simply stay at home as much as possible," the statement concluded.