The Regent's Park Open Air Theatre production of the musical, directed by Jamie Lloyd, was due to begin performances in June.
However the venue has announced today it is to remain closed until at least June 30, as a result of the ongoing coronavirus pandemic.
As a result, producers have cancelled Evita's upcoming run but hope to return to London "soon".
They said in a statement: "In light of the ongoing situation relating to Covid-19, the Barbican will now be closed until the end June. We are therefore sad to confirm that the forthcoming production of Evita has been cancelled.
"All ticket holders will be contacted with regards to refunds, however, as there are a large number of events affected by the venue's closure, we appreciate your patience.
"We are sorry to disappoint our audiences but Regent's Park Theatre, the producers of the show, are working hard to find a way for the production to return to London soon."
Meanwhile, the Barbican said: "To close our building was a poignant moment for us all. We exist to connect people, so we’re still coming to terms with what this means for us as an organisation, as a team, and as a place that welcomes visitors and artists from around the world.
"We’ll be back as soon as we can and are already looking forward to the moment we can reopen our doors. "
Alongside Lloyd, the new transfer was to feature the same creative team as the 2019 Regent’s Park production: sound design by Soutra Gilmour, choreography by Fabian Aloise, musical direction by Alan Williams, lighting design from Jon Clark, sound design from Nick Lidster for Autograph.
The musical Evita reveals the life of Argentine political leader Eva Perón, Argentine President Juan Perón's second wife. The story follows the early life of Evita, her rise to power, work of charity, and ultimate death.
Featuring songs including "Don't Cry For Me Argentina!", "Oh! What A Circus", and "Another Suitcase in Another Hall", productions of Evita won numerous awards including Best Musical at both the Olivier Awards and Tony Awards.