The Ambassadors Theatre Group said its premises undergo regular inspections but further checks were now being carried out following the incident in London's west end on Thursday night which left 76 people injured, seven of them seriously.
More than 700 people were in the Apollo, which was 45 minutes into the National Theatre's performance of The Curious Incident Of The Dog In The Night-time - when members of the audience started screaming as it appeared parts of the ceiling caved in.
Sections of plaster from the Grade II-listed building plummeted on to the stalls below, dragging a section of the balcony with it, striking members of the audience and filling the theatre with clouds of thick dust.
The Apollo's owners, Nimax, said the event was "shocking and upsetting". Nimax does not own any venues in Scotland.
A spokeswoman for ATG said: "ATG is deeply saddened by the tragic incident at Nimax's Apollo Theatre on Shaftesbury Avenue.
"The company's thoughts are with everyone that has been affected and wishes those that were injured a full and speedy recovery.
"All ATG theatres are properly licensed, have appropriate ceiling certificates, receive regular building inspections and have recently undergone full satisfactory condition and structural surveys. ATG continually makes significant investments in the maintenance, upkeep and improvement of its venues to ensure the safety and comfort of its audiences as a top priority.
"As an extra precaution and to reassure our customers, ATG's ceiling contractors have begun additional ceiling and roof surveys within the company's theatres.
"ATG is firmly committed to the best health and safety practices throughout the company and follows strict industry guidelines. ATG's staff all receive regular training in emergency and evacuation procedures."
ATG manages a number of entertainment venues in Scotland, including Glasgow's Theatre Royal and King's Theatre. It also owns the Playhouse in Edinburgh.
Mhora Samuel, from The Theatres Trust, said: "This was a rare thing to have happened.
"The public should be completely reassured that all the theatres in the west end are safe."
It was confirmed yesterday that the Apollo Theatre's health and safety checks are up to date but the investigation has been passed to the Health and Safety Executive (HSE).
All historic theatres and other old buildings are required to undergo a health and safety inspection every three years, although Westminster Council's cabinet member for community protection, Nicola Aiken, said the council may review the three-year rule following the incident at the Apollo.
She added: "All historic theatres have to have regular health and safety checks, and comply with certain health and safety checks for their licence.
"All historic theatres' ceilings are checked every three years. We don't know what the problem is and until we do we can't put a plan into action.
"But we will be working with theatre owners, working with all the other health and safety agencies to make sure, wherever possible, that this doesn't happen again."
Ms Aiken refused to comment on suggestions that extreme weather may have caused the ceiling collapse, adding that officers would leave "no stone unturned" to find the cause.
London Mayor Boris Johnson said the west end is "open for business" as the investigation continues.