Simon Coveney said the radical measures announced today will be a lot for the Irish public to take in.
Schools and childcare facilities in Ireland will close from 6pm today and will not reopen until March 29 to help contain the spread of Covid-19, Taoiseach Leo Varadkar said.
Teaching will be done online or remotely, while state-run "cultural institutions" will close.
Indoor gatherings of more than 100 people and outdoor meetings of more than 500 will be cancelled.
Anyone entering Ireland will be informed of the measures and asked to self-isolate if they are displaying symptoms, the Irish premier added.
Working from home will be encouraged but where people do congregate in offices break times should be "staggered".
Meetings should be done remotely but restaurants, cafes and other businesses can stay open.
"We are asking Irish people to stay apart," Mr Coveney said. "The days and weeks ahead will be difficult and the government cannot do this on its own.
"The most effective tool is to do everything we can to slow down the spread. Those who are vulnerable are precious.
"It will have a deep impact on people's abilities to do their job.
"We are asking people to continue to work where possible. Those who go to the places of work should limit contact."
Museums, galleries and tourist sites in the Republic of Ireland are to close.
People were asked to self-isolate for 14 days if they have symptoms of Covid-19.
The Tánaiste said: "I understand the concerns that many households will have across the country.
"We do need to respond with calm, with unity, with discipline and with resolve, collectively, together.
"This is a phase that we have been planning for for some time.
"These are the right measures at the right time based on the best public health advice, not only in Ireland but in the EU."
Announcing the measures in Washington, Leo Varadkar said: "People should seek to reduce social interactions as much as possible."
The Taoiseach said Ireland will use substantial but not unlimited resources to address the crisis.
He added that acting as one nation could save lives and that the economy will suffer, but "we can bounce back".
"We are a great nation and we have overcome many trials in the past with our determination, and we will prevail again," Mr Varadkar said.