Taoiseach (Irish prime minister) Leo Varadkar said the measures would take effect from 18:00 on Thursday to 29 March.
The first death linked to coronavirus has been recorded in the Republic of Ireland.
The elderly woman died in a Dublin hospital on Wednesday.
Mr Varadkar said schools, colleges and childcare facilities will close from Friday.
He said indoor mass gatherings of more than 100 people and outdoor gatherings of more than 500 people should be cancelled.
He added that where it is possible to work remotely people should do so.
Mr Varadkar said the public and businesses needed to take a sensible approach, adding that the Irish cabinet would meet later and that Northern Ireland and GB would be briefed. (BBC)