It comes as other theatre productions in both the UK and US have shut temporarily due to rising case numbers and the spread of the Omicron variant.
The Hamilton musical on Broadway, New York, cancelled the show just hours before curtain on Wednesday due to “breakthrough cases” of the virus.
Its counterpart at the Victoria Palace Theatre, London said it plans to recommence shows on December 16 at 2.30pm for the matinee.
A statement posted to Hamilton’s Twitter said: “Tonight’s performance of Hamilton on Broadway has been cancelled due to breakthrough Covid-19 cases.
“Our highest priority is always the health and safety of every cast, crew and audience member inside the Richard Rodgers theatre.”
The company apologised for the inconvenience caused and said all tickets would be refunded at point of purchase.
The West End production wrote: “Due to Covid-enforced absences, tonight’s performance of Hamilton can no longer play as scheduled.
“Performances are currently planned to recommence on Thursday 16 December, 2:30pm.
“Patrons affected by this change will be contacted by email in the coming days by their point of purchase, with information on how to exchange tickets into a new performance date or receive a refund.
“On behalf of everyone at Hamilton, we apologise for the disappointment and for any inconvenience this may cause.”
Other Broadway shows affected included The Tina Turner Musical, which was forced to cancel both afternoon and evening performances on Wednesday due to “a limited number” of positive test results within the company.
Harry Potter and the Cursed Child, also playing on Broadway, was forced to cancel its Wednesday matinee but said the evening performance would still go ahead.
In London, the Lion King at the Lyceum Theatre also cancelled shows on Tuesday and Wednesday due to “Covid-enforced absences within our cast and crew” – with performances due to resume on Thursday.
Life Of Pi, based on the Booker Prize-winning 2001 novel by Canadian author Yann Martel, scrapped five shows at Wyndham’s Theatre.
Producers said there had been “several cases of Covid in the company” despite “robust measures taken”.
Performances at the National Theatre of Hex, based on the classic fairy tale Sleeping Beauty, are also cancelled until Thursday.
Meanwhile, The Curious Incident Of The Dog In The Night-Time is cancelled until Friday at the Troubadour Theatre Wembley.
The Royal Shakespeare Company’s The Comedy Of Errors at the Barbican in London has also been halted, with the production hoping to restart on Thursday December 23 ahead of Christmas.
Force Majeure at the Donmar Warehouse was cancelled until Friday following positive coronavirus cases in the cast.
A statement to ticket-holders said: “Due to cases of Covid-19 within the company, performances of Force Majeure Tuesday 14 – Thursday December 16 have been cancelled. We are very disappointed, but the safety of our performers, staff and audiences is our priority.”
The festive period is crucial to theatres for income and reaching new audiences, especially so after most productions were cancelled or delayed in 2020.
This year theatres have been able to stage productions without restrictions on audience capacity.
Many venues have implemented the See It Safely scheme, from the Solt and UK Theatre bodies, which allows venues to display a special mark once they have signed up to a code of conduct and proved they are following the latest guidance.
Approved venues receive a toolkit including the mark, which can be displayed on venues and promotional material, an animated safety video, signage and further training.
Audiences now have to wear masks and show a Covid passport when attending the theatre, following the emergence of the Omicron variant.