Rylance, a former artistic director of Shakespeare’s Globe on London’s Southbank, said Nataasha van Kampen died on Sunday aged 28.
He said: “Our beloved daughter and sister Nataasha passed away of unsuspected natural causes early on Sunday morning.
“Because of our bereavement, I have decided to withdraw from my commitment to the opening ceremony of the Olympics.”
He added: “Claire and I will continue our work with the productions Richard III and Twelfth Night at Shakespeare’s Globe and in the West End.”
It is reported Rylance was due to recite lines from Shakespeare’s The Tempest during the ceremony.
Ms van Kampen was the daughter of Rylance’s partner Claire van Kampen and her former husband Chris van Kampen.
She worked as a film-maker and interior designer in London and New York.
A London 2012 spokesman said: “Our thoughts are with Mark and his family and we of course respect any decision he makes about his role with London 2012 and the London 2012 Festival.”
Rylance, one of Britain’s greatest Shakespearean actors, had also been due to stage “pop-up” performances of the Bard’s sonnets and speeches as part of a three-month arts festival marking the 2012 Games.