The Mater Hospital is appealing to the public, where possible, to avoid its emergency department.
A statement from the hospital on Wednesday morning said that they are "under significant pressure" with capacity.
There have been a high number of presentations to the emergency departments in recent days, and when coupled with an increase in Covid positive patients and a large portion of staff isolating due to contracting the virus or being a close contact, the hospital is facing issues.
The statement continued: "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, any patient who is in need of emergency hospital care will of course be seen and the Mater would urge such patients not to delay and to seek such care.
"Patients who have an appointment at the Mater should attend as scheduled, unless contacted by the hospital and advised otherwise.
"We apologise for any inconvenience this causes and thank the public for their understanding and cooperation."
The Mater is not alone in struggling in recent times, with over 600 people waiting for a bed across Irish hospitals on Tuesday.
INMO General Secretary, Phil Ní Sheaghdha, pleaded with the Government to step in to help.
She said: "The number of patients without a bed in our hospitals today is simply unacceptable and should not be tolerated. The fact that we have over six hundred patients on trolleys while COVID is still a very real feature in our hospitals is inexcusable.
"Since the first week of January in particular, the INMO has been calling for urgent action to ensure that trolley numbers do not rise to unsustainable levels, yet here we are barely the second week of February with a dangerous amount of patients on trolleys."
