The star was to recite a passage from William Shakespeare's play The Tempest at the launch of the sporting spectacular in the British capital on 27 July (12).
However, he will no longer appear in director Danny Boyle's show after his filmmaker stepdaughter Nataasha van Kampen died of "unsuspected natural causes" on Sunday (01Jul12).
The 28 year old was the daughter of Rylance's composer wife Claire van Kampen, who he married in 1992.
A statement from Rylance reads: "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... The family would ask that their privacy is respected at this sad and difficult time."