Mackintosh said the fall had resulted in Sondheim tearing a ligament which has “seriously compromised his immediate mobility”.
The venue – previously known as the Queen’s Theatre – was officially due to reopen on March 14, with a lunchtime reception attended by Sondheim.
“As a consequence, we have had to take the disappointing decision to postpone the official opening of the Sondheim Theatre (where Les Misérables is playing), which Stephen was coming over for from New York. It is likely to be a few months before Stephen will be fit enough to travel to England again to celebrate the new theatre bearing his name,” Mackintosh said.
“Though temporarily incapacitated, Steve is very much still here in feisty frustrated spirit with West Side Story and Company opening imminently on Broadway and the Sondheim Theatre and Sunday in the Park With George opening in London,” he added.
Sondheim joked that he “would do nearly anything for Cameron”, but added: “To stand side by side with him on a West End stage holding onto a stroller is not something I will let him enjoy teasing me about.”
He added: “As I recover from my tumble, I’m impatient to throw away my cane, grab my hat and head across the pond as soon as I can to see on which cherub Cameron has tattooed my initials. I am, to put it mildly, chuffed to have my name on a theatre in the West End I have loved visiting ever since my first trip to London almost seventy years ago. London has always been a second home to me personally and professionally.”