The Oscar-winning actor said in a statement that his brother, Jonathan Waters, was knocked off his bike last month and later died from his injuries.
Sir Mark said three forthcoming performances of the play on June 11 and 12 have had to be cancelled so he can attend the funeral in California, as there is no understudy for his lead role of Johnny “Rooster” Byron.
The 62-year-old said in a statement: “I am so sorry to tell you that on the 28th of May my dear brother Jonathan Waters was knocked from his bicycle and tragically died of his injuries.
“In order to attend his funeral in California, I unfortunately have to miss three performances of Jerusalem over Saturday 11th – Sunday 12th June.
“As I have no understudy as Rooster Johnny Byron, sadly these performances have been cancelled.
“Sonia Friedman Productions, together with Nimax, are arranging additional performances at the end of the scheduled run to try and accommodate everyone who will be affected.
“I hope you understand my need to grieve my beloved brother, and thank you for your support at this time.
“I hope you will be able to attend another performance of Jerusalem.”
Sonia Friedman Productions, Nimax and the company of Jerusalem offered their support and thoughts to Sir Mark at this time.
Additional performances have been added on Tuesday August 9 at 1.30pm and 7.30pm and Wednesday August 10 at 1.30pm to accommodate those who were due to attend the cancelled performances.
Organisers have said all affected customers will have exclusive access to exchange their tickets for these performances on a first come, first served basis.
They added: “We sincerely apologise for any inconvenience this may cause you and look forward to welcoming you to an alternative performance.”
Sir Mark first starred as brutish Johnny “Rooster” Byron in Jez Butterworth’s play at the Royal Court Theatre in 2009.
The following year, the production moved to the Apollo Theatre and Sir Mark went on to win the best actor Olivier Award for his role.
Eleven years after its successful run, Jerusalem returned to the West End in April, with Sir Mark reprising his role alongside Pirates Of The Caribbean actor Mackenzie Crook.