The European Champions Cup and Challenge Cup have been temporarily suspended.
The move comes after the French government recommended that games against British clubs be postponed amid the COVID-19 crisis.
European Professional Club Rugby said n a statement it had no choice but to suspend games for the time being.
"Following a directive from the French authorities that the participation of TOP 14 clubs in the Champions Cup and Challenge Cup at the current time constitutes too great a public health risk, EPCR has no choice but to announce that the 2020/21 tournaments are temporarily suspended."
However, EPCR aims to resume and finish the tournaments "as soon as practicable".
Tournament chiefs hope two rounds of Heineken Champions Cup and Challenge Cup pool games on the weekends of 15-17 and 22-24 can go ahead at a later date, as authorities deal with the impact of a new strain of coronavirus.
Bristol director of rugby and former Blues coach Pat Lam has suggested that if European games are postponed, Premiership fixtures should be brought forward to fill the gap to avoid "cramping up fixtures later on".