The Pro14 has been suspended indefinitely because of the coronavirus outbreak.
Round 14 of the competition for clubs from Scotland, Ireland, Wales, Italy and South Africa was due to take place next weekend, starting 20 March.
There was already disruption involving the Italian teams, with Ospreys' trip to Zebre and Ulster's game at Benetton both postponed on 29 February.
Pro14 says the resumption of the season will be "a matter of constant review".
"We have made this decision with everyone's welfare foremost in our minds," said tournament director David Jordan.
"With an evolving situation in the five countries that take part, it is important to make a clear decision in keeping with the advice of the various governments involved."
Unbeaten Leinster are top of Conference A, with Edinburgh leading Conference B.
With travel restricted across the whole of Italy, Zebre were not allowed to travel to face to Cardiff Blues on 21 March, and Benetton were unable to go to Munster the following week.
Benetton had been given permission to travel to Newport on 6 March to take on Dragons after giving assurances none of their players or staff had been in contact with anyone suffering from the illness.
The final of the competition is due to be played on 20 June at the Cardiff City Stadium.
Scotland's First Minister Nicola Sturgeon has advised gatherings of more than 500 people should be cancelled.
The Six Nations has already been impacted, with two of the final-weekend matches postponed - but Wales' match with Scotland in Cardiff on Saturday is due to go ahead as planned.