The final two rounds of the European Champions Cup and Challenge Cup will be cancelled and the tournaments will move straight to the knockout rounds, Premiership Rugby chief executive Darren Childs said.
The French government blocked Top 14 clubs from competing in the European competitions against clubs from United Kingdom and Ireland over the next two weekends due to COVID-19 concerns.
European Professional Club Rugby (EPCR) initially decided to suspend the matches but Childs said the decision had been taken to scrap them due to a lack of space in a congested schedule.
"The reason we can't reschedule those is that there are no available weekends. Our season is now full right until our final," Childs told British media.
"It was decided very quickly by all three leagues [Premiership, Top 14 and PRO14] that we would complete the tournaments in the last four weekends [in April and May]."
Childs added the EPCR are set to announce a revamped structure of the competitions in the coming weeks.
Following the French government's directive, English Premiership opted to implement a two-week break rather than bring forward domestic fixtures to fill the empty weekends.
The Premiership said it decided not to change the league's existing schedule to protect the welfare of players and staff.
"We've had 70 players in the last three weeks who have tested positive with COVID, and in that period of time we lost five games," Premiership Rugby director Phil Winstanley said.
"It made absolutely no sense to bring games forward from later in the season to this period of time, when it is our highest [virus] prevalence and our highest risk."