The Mater Hospital has asked people to avoid its emergency department "where possible".
Management of the Dublin hospital says it is under "significant pressure" due to a high number of emergency presentations, as well as COVID-related issues.
In a statement, the hospital said: "The hospital is under significant pressure due to a combination of high presentations at the ED, and an increased number of COVID positive patients in the hospital, as well staff who cannot come to work due to contracting COVID or being a close contact.
"Where possible, the Mater Hospital advises patients with non-emergency conditions to seek assistance from other parts of the health service such as minor injury units or their GP.
"Unfortunately, those who do present at the ED with non-emergency conditions can expect long waits."
However, they add that any patient who needs emergency hospital care will be seen and that any such patients should not delay in seeking care.
Patients who have an appointment at the Mater are being advised to attend as normal "unless contacted by the hospital and advised otherwise".
Mater management apologised to the public for any inconvenience the issues will cause.
Figures released by the HSE overnight showed the Mater had the most COVID-19 patients of any hospital in the country.
65 patients with the virus are being treated at the hospital - around 10% of the total number of patients with COVID currently in Irish hospitals.
INMO trolley figures, meanwhile, show 31 patients in the Mater's emergency department are waiting for a bed this morning.