The pair were set to meet on October 26 on the undercard to the World Boxing Super Series super-lightweight final between Josh Taylor and Regis Prograis.
Promoter Eddie Hearn tweeted: “Due to illness, Joseph Parker is out of the Dereck Chisora fight on October 26. We are working on a suitable replacement and will make a further announcement this week”.
Chisora, 35, had complained last month about not being the main event of the London show.
He said: “Give me main event or pull me out of the show. I’m not going to sell out the O2 for them guys to be the main event.
“I’m being serious, you want me to sell it out to the London crowd, my London fans, then put these little guys that no one knows about on my show and mug me off.
“I’m taking the main stage, if not I want more money.”
Chisora has won 31 of his 40 career bouts while Parker’s two defeats both came on British soil in 2018 – against Anthony Joshua in Cardiff and Dillian Whyte in London.