The 85-year-old actor was performing in Player Kings earlier this month at the Noel Coward theatre when he fell into the audience.
The production had been due to go on tour until 27 July but Sir Ian, 85, has announced his withdrawal with the “greatest reluctance” to “protect my recovery”.
A statement from the production said: “Following Ian McKellen’s injury during the West End run of Player Kings, his doctors’ advice is to take time off from work in order to fully recover.
“As such, he will not be returning to play Sir John Falstaff in the national tour of Players Kings (3-27 July 2024).
“Ian continues to recuperate very well, but he needs the time to rest and ensure a complete recovery. We continue to send him our best wishes.
“As it was for the final West End performances, the role of Falstaff will now be performed by David Semark, Ian’s brilliant understudy, for all tour dates of Player Kings.”
Sir Ian had been playing Sir John Falstaff – one of Shakespeare’s most famous creations – in the modern reworking of Henry IV, parts one and two.
The Olivier Award-winning star said in a statement: “Two weeks after my accident onstage, my injuries improve day by day.
“It’s with the greatest reluctance that I have accepted the medical advice to protect my full recovery by not working in the meantime.
“I had been so looking forward to bringing Player Kings to theatre-goers in Bristol, Birmingham, Norwich and Newcastle.
“But I can assure them that, with David Semark now playing Falstaff, Robert Icke’s production and his acting company remain as dazzling as ever. Go see for yourself!”
Sir Ian lost his footing during a fight scene in the play involving the Prince of Wales and Henry Percy.
The Lord Of The Rings star was heard crying out in pain as staff rushed to help, and the theatre was quickly evacuated.
Sir Ian said he spent three days in hospital following the fall before undergoing “physiotherapy, light exercise and a lot of essential rest at home”.
He also thanked well-wishers for their messages of support, as well as the NHS experts who had diagnosed and treated him.
Following its West End run, the play begins a national tour, starting at the Bristol Hippodrome on Wednesday 3 July, before stops in Birmingham, Norwich, and Newcastle.
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