Hamilton, Les Miserables, Mary Poppins and The Phantom of the Opera will not return to London's West End until 2021, their producer has announced.
Sir Cameron Mackintosh said "drastic steps", including redundancies, were required if the shows are to reopen "as early as practical" next year.
Culture Secretary Oliver Dowden said he would ask leading performers to help draw up a plan for theatres to reopen.
But he acknowledged venues face "very specific and practical obstacles".
Speaking at the government's daily press briefing, Mr Dowden said he would bring together "our leading performers in theatres, choirs and orchestras with medical experts and advisers".
He continued: "The idea is that they will work together in detail to develop that roadmap which is so badly needed to performing safely - with a particular focus on piloting innovative ideas that may permit live performances."
Mr Dowden said Sir Cameron was one of "dozens of people" he had consulted about the challenges facing the creative industries.
But he admitted it would be "exceptionally difficult" for venues to reopen from 4 July, which is the current scheduled date for stage three of the government's reopening plan.
In an earlier statement, Sir Cameron earlier said the government had yet to offer "tangible practical support" to the theatre industry or say when social distancing would be lifted.
This, he said, made it "impossible for us to properly plan for whatever the new future is".
It is not known how many jobs are at risk from the closure of his four productions. "This decision is heartbreaking for me, as I am sure it is for my employees," he said.
Which musicals are affected?
- Hamilton, about American founding father Alexander Hamilton using rap and hip-hop, has been running at the Victoria Palace since 2017. A filmed version of the original Broadway production will premiere on the Disney+ streaming service next month.
- Mary Poppins, an adaptation of PL Travers' stories about the flying nanny and the 1964 Disney film, first opened at the Prince Edward theatre in 2004. The current revival, at the same theatre, opened in October 2019.
- Les Miserables, based on Victor Hugo's 1862 novel, has been a West End staple since 1985. Its current production has been running at the Stephen Sondheim Theatre, formerly the Queen's, since December 2019.
- The Phantom of the Opera, Andrew Lloyd Webber's adaptation of Gaston Leroux's 1910 novel about a scarred musical genius living beneath Paris's Opera House, has been running at Her Majesty's Theatre since September 1986.
"The commercial theatre provides billions of pounds of revenue to the economy," Sir Cameron continued.
"It is time this is recognised and the government takes action to ensure this priceless resource... is helped to survive."
His four musicals were among many West End shows forced to close at the beginning of the coronavirus lockdown.
Three months on, it remains unclear when and how London's Theatreland can resume operations safely and profitably.
Sir Cameron's statement follows news that Nimax Theatres is to begin making some of its staff redundant. Around 130 jobs are believed to be at risk, according to the Broadway World website.
Around 60 members of staff at the Birmingham Hippodrome may lose their jobs as a result of the coronavirus pandemic.
Jobs are also at risk at the Wales Millennium Centre in Cardiff, which could remain closed until April next year.
Research commissioned by the Creative Industries Federation suggests more than 400,000 jobs in the sector could be lost.
"Without additional government support we are heading for a cultural catastrophe," its chief executive Caroline Norbury said.