The Health Service Executive (HSE) is advising people to stay home and, effectively, act like they have COVID-19.
It says this is in response to the high prevalence of coronavirus in the community.
This will also see changes in the testing and tracing system, which means close contacts of a confirmed case will no longer be referred for a test.
The HSE says this step is being taken "to ensure that those who are symptomatic are prioritised and receive a test as quickly as possible."
It comes as 1,620 new confirmed cases of COVID-19 were reported here on Thursday, with Ireland "no longer in a containment phase".
HSE Chief Clinical Officer, Dr Colm Henry, explains: "We are asking all close contacts to restrict their movements - this is the strongest defence we have against the spread of this virus.
"If you show any symptoms please call your GP or GP Out of Hours service immediately, and they will refer you for a test if required.
"We know that GPs and GP Out of Hours services are very busy, and we ask for everyone's patience as we all work through this challenging time.
"We are asking that the public support this measure fully and follow all public health advice so that we can all keep our friends and family safe."
Dr Henry adds: "The pressure on our public health system, including testing and tracing services is not sustainable.
"A collective response by every individual, across every county, to follow the public health advice is essential to address the recent acceleration in case numbers that we are now seeing."
While people who received notification by SMS that they are a close contact should follow the existing public health guidance and restrict their movements for 14 days.
If they become symptomatic, they should call their GP and arrange a test.
The text message for close contacts will now advise a person that they are a close contact, and that they should restrict their movements.
The HSE says the measure is temporary "to ensure those who are symptomatic are tested as quickly as possible and that we can continue to try to reduce the spread of the virus."
