Stoke get their pre-season Barclays Asia Trophy tournament with a clash against the Toffees in Singapore on Wednesday.
The Potters will have most of their star players present for the match but manager Mark Hughes has revealed that the central defensive pairing of Shawcross and Wollscheid will be missing due to back and hamstring problems respectively.
"Both players have been working out here, but they aren't fit and ready for minutes as of yet," Hughes told Stoke's official website.
"Ryan has a little bit of trouble with his back, which will hopefully clear up quickly, while Philipp has had a bit of stiffness in his hamstring.
"They will both be working with the physio tomorrow, but they won't be involved in any capacity for the game. It would be silly of us to put them at risk on Wednesday, so we will hopefully look to get them involved in the second game on Saturday evening."