The Grand Slam event was to have taken place from May 24 to June 7, but organizers said: "The current confinement measures have made it impossible for us to continue with our preparations and, as a result, we are unable to hold the tournament on the dates originally planned. "
The new dates would mean the tournament would start just one week after the US Open, If that event remains in its scheduled slot.
"The whole world is affected by the public health crisis connected with COVID-19. In order to ensure the health and safety of everyone involved in organizing the tournament, the French Tennis Federation has made the decision to hold the 2020 edition of Roland-Garros from 20th September to 4th October 2020, "read a statement.
"In order to act responsibly and protect the health of its employees, service providers and suppliers during the organization period, the FFT has chosen the only option that will allow them to maintain the 2020 edition of the tournament while joining the fight against COVID-19 . "
FFT president Bernard Giudicelli said: "We have made a difficult yet brave decision in this unprecedented situation, which has evolved greatly since last weekend. We are acting responsibly, and must work together in the fight to ensure everybody's health and safety."
Last week, the ATP announced it was suspending the men's tennis tour for six weeks "due to escalating health and safety issues" arising from the spread of the virus.
All events on the ATP Tour and second-tier ATP Challenger Tour are canceled until April 27.
The International Tennis Federation, which runs the lower tiers of the professional game as well as the junior and senior circuits, followed the ATP by announcing there would be no tournaments on any of its tours until April 20 at the earliest.
The WTA Tour said Monday it was suspending the women's season until May 2, having already called off events in Bogota, Guadalajara and Charleston.
Next month's Fed Cup finals in Budapest have also been postponed indefinitely.
The revamped 12-team women's competition scheduled for April 14-19 as well as a series of play-off ties were both put on hold.