Filmhouse has suspended operations and EIFF is postponed Photo: Max Crawford
On Twitter, the festival said it is "looking at which elements of the Festival can be delivered later in the year".
The festival is the latest to fall victim to Covid-19, with others including SXWS, Tribeca and BFI Flare. Most cinemas in the UK have now closed till further notice, with Tyneside Cinema also announcing suspension today.
The closure of Edinburgh Filmhouse and Belmont Filmhouse in Aberdeen until further notice was also announced.
The festival tweeted: "Our first priority is the health and wellbeing of our staff, filmmaker guests and audiences, and we wish you all health and strength through this difficult time.
"Tickets purchased online for future screenings will be automatically refunded, however at this challenging time for the Filmhouse and Belmont cinemas we would ask you to consider converting your refund into a donation towards sustaining our charity and our future work.
"For tickets purchased at the Box Office, refunds will be available to customers when we re-open. Memberships will be frozen until we are able to resume operating, but if you are able to consider continuing your membership payments it would be a significant support."
The festival had been due to hold its 74th edition from June 17 to 28.
On Twitter, they added: "We look forward to a brighter time when our cinemas can bring us all back together in a shared celebration of film, and its role in giving us a window on the best and most diverse stories and story tellers from across the world.
"Meanwhile we’ll be doing our best to keep everyone’s spirits up and conversation going through our social media and digital channels and hope that many of you will engage with us, retaining what we can of our sense of community and sharing our passion for film."
Edinburgh International Film Festival CEO Ken Hay said: “It is with huge regret that we have taken the necessary decision to postpone the 74th Edinburgh International Film Festival. Film festivals are critical platforms for films and filmmakers to reach and engage with audiences, and EIFF has done this uninterrupted for 74 years. However the health and wellbeing of our staff, filmmaker guests and audiences has to be the first consideration.
“We are looking at which elements of the Festival may be delivered later in the year and we will keep you informed as plans develop. For now, we would like to thank our funders, sponsors, partners, staff, donors, patrons, filmmakers, sales agents, distributors and audiences for their loyalty, support and understanding in these unprecedented times.”