Ministers in Ireland faced sharp political and business resistance to what would have amounted to Europe's first major second-wave national lockdown.
McGuiness will be replacing Phil Hogan who resigned following the controversy on his movements while in Ireland which were in breach of Covid-19 rules.
Arrivals into Ireland from Malta, Finland, Norway, Italy, Hungary, Estonia, Latvia, Lithuania, Cyprus, Slovakia, Greece, Greenland, Gibraltar, Monaco, and San Marino will not have to restrict their movements.
Spanish archaeologists may have uncovered the final resting place of an Irish nobleman whose bloody 16th-century rebellion almost toppled Ireland's English rulers.
Conlon's personal 'popemobile' was used by Pope John Paul II on trips to Britain and South Africa in the 1980's.
Because we stand by our Italian friends. We can only manage this together. German Foreign Minister
The move comes just two days before the country's national day, St Patrick's Day, which traditionally sees bars across the country packed from early in the day. The annual parade celebrating the day had already been cancelled.
President Donald Trump has taken a coronavirus test but said on Saturday that his temperature was "totally normal", and his administration extended a travel ban to Britain and Ireland to try to contain a pandemic that has shut down much of the daily routine of American life.
Ireland has so far reported 24 cases after three more were identified on Monday, among over 110,000 globally. Ireland's chief medical officer said that while the country was still containing the virus, it would eventually move into the stage of delaying its transmission and mitigating the impact.
Irish Prime Minister Leo Varadkar on Tuesday called a parliamentary election for Feb. 8, pitting his record on Brexit and Ireland's fast growing economy against struggling services in a contest polls suggest is too close to call.