President Bernard Laporte said the FFR had called for a stop to all rugby union for an indefinite period as an "essential act of solidarity" with the rest of France.
The France men's national team's Six Nations match against Ireland, which had been due to take place this weekend at Stade de France, had already been postponed.
France's top professional league, the Top 14, had intended to play matches behind closed doors, but the FFR ruling ends that immediate prospect.
Former national team coach Laporte said: "The French Rugby Federation, a delegate of public service and depositary of the values on which our society is founded, contributes to the national solidarity to fight against the spread of the virus which is currently hitting our country.
"It is our responsibility to take the necessary decisions in line with the announcements developed by the president of the republic.
"Consequently, the FFR suspends from today all its competitions, gatherings and training, as well as those of its leagues, departments and clubs, until the sanitary conditions allow their resumption.
"All championships, of all categories without exception, are suspended, as well as all activities of rugby schools, in order to effectively combat the spread of COVID-19.
"We ask our entire network to scrupulously respect these instructions, which are of very high national interest."
Laporte added: "The contribution of French rugby will be flawless."