The joint decision was taken following France's ban on events with large gatherings until mid-July.
"The Directors' Fortnight, La Semaine de la Critique and ACID regret to announce the cancellation of their 2020 editions in Cannes," Variety quoted the statement from a release.
"The health crisis we are all presently facing makes it impossible to anticipate the practical course of events," the release further read.
However, "each section, in consultation with the Cannes Film Festival, is looking at the best way to keep on supporting the films submitted to its 2020 edition," added the release.
Meanwhile, a plan for a virtual version of the Cannes film market, the Marche du Film, might be going ahead in June.
The Marche du Film is now setting up a full-on virtual market from June 22-28, confirmed Variety.
Jerome Paillard, head of the Marche du Film, is to communicate details about the virtual market on Friday.
However, on April 8, The Cannes film festival director Thierry Fremaux has confirmed that the major event won't take the virtual route if it can't be hosted as a physical event.
( With inputs from ANI )