Leo Varadkar has said that the elderly and people who have a long-term illness may have to stay at home for several weeks.
The Taoiseach (prime minister) said that the Republic of Ireland is putting in place systems that people in this category will have food supplies and are checked on.
Mr Vardkar said this is known as cocooning.
He added: “This is the calm before the storm, before the surge.”
The total number of coronavirus cases in the Republic of Ireland has now reached 292.
This represents a rise of 69 new confirmed cases of Covid-19.
The Irish Department of Health said the cases announced on Tuesday are made up of 29 males and 40 females
Two people have died from Covid-19 in the Republic of Ireland and Taoiseach (Irish Prime Minister) Leo Varadkar has said the country would be dealing with the emergency for months to come.
The Health Service Executive in the Republic has said it is now “working rapidly to identify any contacts the patients may have had, to provide them with information and advice to prevent further spread”.
Dr Tony Holohan, chief medical officer, said: “Co-operation across the health service has never been more important and I would like to thank our colleagues in their ongoing efforts to help us to prepare for and limit the spread of Covid-19.”
On Tuesday, the Irish cabinet signed off on a number of measures that would allow people to be detained on foot of a medical recommendation if they have Covid-19 and refuse to self-isolate.
The measures will also give the Irish government the legal power to shut down mass gatherings.
They are to go before the Dáil (Irish parliament) on Thursday.
RTÉ reports that the legislation will also enable special welfare payments for those who cannot work as a result of Covid-19.
A full-time Public Order Unit is being established by gardaí (Irish police) in response to the coronavirus outbreak.
It is to be tasked with patrolling key public order risk locations, the protection of life and property, the maintenance of law and order, emergency response as well as dealing with any protests or public order issues.
The total number of tests completed is 1,338.