The HSE said "less than 100" patients who were told by text they had tested negative for Covid-19 were later told their test was positive.
In a statement, the Executive said it happened because a small number of tests were "weakly positive" and had to be sent for review.
It said the communications error was picked up by public health doctors and immediately rectified -- and that no other patients have been affected.
The HSE said it is investigating after people were told by text they had tested negative for Covid-19 but were later told their test was positive.
HSE chief executive Paul Reid said it is not clear how many people got the wrong texts.
He said the issue only emerged yesterday.
Mr Reid said: "We particularly have been dealing with an issue that emerged over the weekend where some people have got a negative and then got a call to say it was positive etc,
"That is something that we are just working through right now to get further detail behind it and we will communicate further."
Meanwhile, the Minister for Health Simon Harris said social distancing could be part of Irish life until a vaccine for coronavirus is available.
Simon Harris said there is "no magic point" at the start of May where life before Covid-19 can resume.