The Lord Of The Rings actor, 85, who is playing John Falstaff in a production of Player Kings at the Noel Coward Theatre, was in a fight scene when he lost his footing and fell from the stage during Monday evening's performance.
"Thank you to our audience and the general public for their well wishes following Ian's fall during this evening's performance of Player Kings," a spokesperson for the London theatre said in a statement to the PA news agency.
"Following a scan, the brilliant NHS team have assured us that he will make a speedy and full recovery and Ian is in good spirits.
"The production has made the decision to cancel the performance on Tuesday June 18 so Ian can rest. Those affected will be contacted by their point of purchase as soon as possible tomorrow."
The statement also thanked doctors Rachel and Lee who were "on hand in the audience" and to the venue staff "for their support".
After the accident, audience members were informed that the remainder of the evening performance had been cancelled and they were evacuated from the premises.
A BBC journalist, who saw the play, said the veteran stage and screen actor was in a scene involving the Prince of Wales and Henry Percy when he fell off the front of the stage.
The actor was heard to cry out in pain as staff rushed to help.
Audience member Paul Critchley told PA it was a "shock" to witness the fall.
Critchley, a Methodist minister from Downham Market, Norfolk, said: "Sir Ian seemed to trip as he moved downstage to take a more active part in the scene.
"He picked up momentum as he moved downstage which resulted in him falling off the stage directly in front of the audience.
"The house lights came up very quickly as the stage management and front of house team dealt with the incident. We were evacuated immediately so that Sir Ian could be treated in privacy.
"An announcement was made by theatre management that the show had been cancelled, that Sir Ian was receiving treatment and an ambulance had been called.
"It was a shock to witness his fall and I wish him a speedy recovery. My thoughts are also with his fellow cast members, stage crew and front of house team at the Noel Coward Theatre."
London Ambulance Service has declined to comment.
Sir Ian's career has spanned more than six decades and seen the actor perform at theatres around the country.
On screen he is most known for playing Magneto in the X-Men films and Gandalf in Peter Jackson's fantasy trilogy, based on the books from JRR Tolkien.
On the stage he has played a number of Shakespearean characters including Richard II, Macbeth, Coriolanus, and King Lear.
His many acting credits have led to a number of accolades over the years including several Olivier Awards.
