The 'Lord of the Rings' legend -who celebrated his 85th birthday in May- was hospitalised on June 17 after losing his footing during a performance of 'Player Kings' at the Noel Coward Theatre on London's West End, which saw him plunge from the stage into the audience.
He has since been forced to withdraw from the Shakespeare production, but he has now told fans he is "on the mend".
He wrote on X, formerly Twitter: "Just two weeks after my accident onstage I want to assure my many well-wishers that the injuries (to wrist and neck) are on the mend".
"My doctors promise a complete recovery -but only if I avoid work over the next few weeks".
The veteran actor confirmed his understudy David Semark will take on the role of drunken raconteur John Falstaff on the company's upcoming four-week tour, after replacing him for the final West End performances "with panache".
Meanwhile, McKellen admitted it felt "somewhat shameful" to be missing shows, even though it's not his fault.
He continued: "Any actor will say that missing a performance feels somewhat shameful, even when he is not to blame".
"None of us ever wants to let down our audience. But Robert Icke's masterful production remains intact".
"His mis en scene is compelling throughout and his actors, led by Toheeb Jimho and Richard Coyle as Prince Hal and his father, remain on top form. Go see for yourself!".
After his fall, the rest of Sir Ian's performances for the last week of 'Player Kings' run in in London were cancelled to allow him to rest.
The production came to a finish in the city on 22 June, but Sir Ian was expected to rejoin the cast when the play started on its UK tour with a show in Bristol on 3 July.
Earlier this week, he said: "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".