Jones scored the opener in the Potters' 3-1 Carling Cup defeat at West Ham on Wednesday night, but was taken off with a high temperature.
The same bug which has swept through the Stoke camp then accounted for Pennant, who also came off during the second half.
City boss Tony Pulis said: "It's a case of dusting the players down and getting them ready for Everton after the disappointment of losing a long match like this.
"We're hoping Kenwyne and Jermaine Pennant will be all right because they were both feeling under the weather and had to come off.
"There has been something going around the camp. Kenwyne didn't really want to play, but I gave him a bit of a cuddle to get him out there.
"He felt very sweaty and cold. He said he'd had it over a week now, but he'd said nothing about it before."