There are calls for serial testing in meat plants to be reintroduced immediately.
It has been suspended to an increase in demand for Covid-19 testing elsewhere.
The mass testing started two weeks ago and 40 people have tested positive since.
In a statement, the HSE said that Covid-19 testing of staff at meat and food processing facilities is being "re-scheduled into next week".
This was a "precautionary measure" to allow the health service focus its resources on meeting the "significant rise in demand for testing among people with coronavirus symptoms in the community".
Testing demand "nearly trebled on Monday" with a requirement for over 13,000 community tests and over 3,000 hospital tests.
Speaking to Midwest News this Lunchtime, Roscommon Independent Deputy Michael Fitzmaurice has described the move as surprising and disappointing.