Prime Minster Boris Johnson told a briefing on Monday that the UK has moved into another phase in the outbreak and people should avoid "non-essential" travel and contact with others.
Therefore, the 15-man code has followed the majority of the sporting world to close down until the situation is clearer.
The Pro14 and Top 14 leagues were suspended last week and now the Premiership has followed suit, with the resumption pencilled in for the weekend of April 24-26.
European rugby has also been affected, with the quarter-finals of the European Champions Cup and Challenge Cup postponed.
The decision on the European matches was taken after a conference call of the Board of European Professional Club Rugby (EPCR) and they are hopeful of completing the campaign.
A statement said: "While respecting all further directives by governments and local authorities, EPCR remains committed to trying to find a solution which will enable it to complete the 2019-20 Champions Cup and Challenge Cup tournaments at such a time as that aligns with preventative measures undertaken by an overwhelming majority of sport's governing bodies and tournament organisers in Europe."