The two other scheduled games in round five had already been postponed and no dates have been confirmed for completing the 2020 Championship.
The Welsh Rugby Union, which had insisted earlier on Friday the game would go ahead, said it was "in the best interests of supporters, players and staff to fall in line with recent measures taken across the UK and global sports industries".
A WRU statement read: "The Welsh Rugby Union has maintained an open dialogue with, and continued to seek advice and direction from, the Welsh government and other stakeholders, including the Six Nations, on this fast-moving issue.
"Every effort has been made to stage this game and we appreciate that individuals will have been inconvenienced. Given the fluid and unprecedented nature of this issue a postponement became the only viable option."
Friday's U20 Six Nations match between Wales and Scotland in Colwyn Bay will go ahead but will be played behind closed doors.
Meanwhile, Scottish Rugby has suspended all rugby in Scotland for the remainder of March.
A Scottish Rugby spokesperson said: "We have taken on board all expert medical advice before now and we are taking a precautionary approach to give time to assess what the impact of coronavirus will be on Scottish society in the coming weeks before deciding on next steps.
"This decision has been taken with the best interest of everyone involved in the game and in support of the country's work to address the impact of Coronavirus."