They have not yet decided how that will affect clubs who looked set to be promoted or relegated.
The RFU's move comes a day after football authorities postponed all games up to April 30 but said they may extend the deadline for finishing the season beyond June 1.
The rugby news was relayed to clubs and fans in a message from RFU CEO Bill Sweeney on Friday morning. He said: "My thoughts and those of all of us at the RFU are with everyone impacted by COVID-19 as well as recent flooding events, both across the country at large but also within our own rugby union community.
"In order to provide clarity and to assist with immediate and longer term planning, the Rugby Football Union is announcing the end of the 2019/20 rugby season for all league, cup and county rugby in England. The only exception to this is the Gallagher Premiership, who we are in active discussions with to review possible best next steps.
"When current government advice on social distancing measures changes, we will naturally encourage rugby training and friendlies to recommence.
"I would like to personally thank everyone for their swift actions in suspending rugby activity, this is not an easy time and I know many of you will have concerns that go beyond the game.
"We are working through the implications of ending the season early and have instigated a thorough process to ensure fair and balanced outcomes for the game. We will communicate these outcomes by the middle of April. While we would like to provide all the answers now, we need some time to get it right for the best interests of the game. Rest assured we are working on this as a priority and we will continue to send weekly updates to clubs."