The fight was set to take place as co-main event at London's 02 Arena.
The 26-2 Parker has had just one fight in 2019, a TKO of Australian Alex Leapai in Providence in June.
ESPN reporter Dan Rafael reported that Parker had been ill for much of the last week and has been unable to train.
According to Rafael, Parker's camp believe the illness was caused by a spider bite.
Parker's manager David Higgins earlier told the Herald that trainer Kevin Barry had identified a "sore" in the fighter's thigh as soon as he got into camp, and thought it looked like a spider bite.
While the origin of the infection has not been confirmed as a bite, a "physician in Las Vegas said Parker was in a bad way and stood him down for three weeks".
Higgins said Parker was upset at having to withdraw from the Chisora fight, but has chosen to stay in camp and fight again as soon as possible.
"We'll leave it up to his promoter Eddie Hearn to get him on the next possible card," Higgins said.
The fight against Chisora is one that Parker and his team want. Once medical clearance is given, Parker wants the fight promptly rescheduled.