There are no appointments available at any of Cork's five PCR testing facilities.
It comes as calls are made for PCR testing capacity to be increased.
No appointments are available for numerous test centres around the country, with GPs calling for more walk-in community testing centres.
3,666 cases of COVID-19 were detected yesterday, while 638 patients with the virus are in hospital - including 130 in ICU.
Social Democrats co-leader Roisin Shortall says while testing capacity has increased in recent days, it's still not meeting demand.
"The advice to people is to do the right thing, get tested when you get symptoms, and where people go to do that - it's not possible.
"What that results in then is that very often those people instead of self isolating will continue to plough on, and hope that it's just a flu or something like that."
The Deputy Chief Medical Officer has said no health service in the world could deal with the current demand for PCR testing.
Dr Ronan Glynn says at the moment demand is far outstripping availability.
"It appears that somewhere between 10-20% of adults and children in this country in the last wee have flu or Covid-like symptoms, so that's about 700,000 people in the past week who have had symptoms.
"There's no testing service in the world that's going to be able to service that demand."
