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The Nutcracker, which is running at the Festival Theatre, was due to close on December 31, with Sleeping Beauty set to run until January 15.
Fiona Gibson, Chief Executive of Capital Theatres Trust, which operates both venues, said: “We are devastated to find ourselves in a position where keeping the King's and Festival Theatres open is simply not viable for this period, especially after we have worked so hard to build our business back up after 15 months of darkness.
“It's a huge disappointment for our staff, the artists on stage and of course audiences for whom a visit to the theatre is often a highlight of the holiday period. A small consolation is that we can continue to entertain our youngest audience members in the studio with The Enormous Christmas Turnip.
“These closures, which come at our busiest time of year, will have serious financial implications and we urge Scottish Government to clarify and administer the support available to the cultural sector as quickly as possible. Significant funding is needed to ensure that when we emerge from this latest pandemic crisis Scotland still has a theatre industry to cherish.”
All customers booked into one of the affected performances will be contacted by box office and offered a credit note or a refund. The Enormous Christmas Turnip in The Studio will still proceed under the new regulations and will continue until the end of its run on 31 December with one metre social distancing in place.
The new restrictions which limit indoor events to 200 people if seated and 100 for standing will also see most of the city's live music programme decimated and impact on Musselburgh's Brunton Theatre's Hansel and Gretel, which was also due to run until Hogmanay.
Producers of the panto, which has just resumed its run after a cast member tested positive for Covid, are looking at the viability of continue the run from Boxing Day with socially distanced audiences.
A spokesperson for the theatre said: “The Brunton has strict Covid measures in place for the safety and well being of our staff, performers and audiences and this is our highest priority. We comply with all of the Scottish Government’s Covid 19 guidance on operating safely and will continue to do so.
"Scottish Government’s updated Covid-19 guidance stipulates that from 26 December for three weeks, indoor live events will be restricted to a maximum of 200 people with social distancing of one metre.
“The Brunton presented socially distanced live performances in 2020. We are contacting all customers who have purchased tickets for one of our performances of Hansel and Gretel from 26 to 31 December 2021 with a view to assessing the viability of presenting socially distanced performances of Hansel and Gretel.”
The clamp down caused by the rise of infections from the Omicron variant will see the closure of the Capital's theatre-land for a second Christmas and New Year period after a five week run of White Christmas at the Edinburgh Playhouse was curtailed earlier this week due to Covid infections within the company.
The Greenside Place venue, which also hosts one night events, responded to the new regulations stating: 'We are busy reviewing the Scottish Government’s latest Covid guidelines and the impact it has on our venue and performances. We’d like to thank our customers for their patience and support throughout this time. We will share an update as soon as we can.'
The Royal Lyceum and Traverse theatres had already cancelled their productions of Christmas Dinner and Wilf, again due to the impact of the coronavirus.