"Jack (Wilshere) felt a pain in his ankle two days ago and he will not play at the weekend," Pellegrini told reporters ahead of Sunday's visit to Goodison Park.
"We should know more after the medical review in the next few days."
Mexican striker Javier Hernandez is also unavailable having missed a week of training through illness.
The injuries come as a blow for West Ham, who have lost all of their four league matches this season.
Pellegrini insists he remains dedicated to the project and that he retains the full backing of the board.
"I know the way they think, the owners and (vice-chairman) Karren Brady," the Chilean added.
"I spoke with all of them before I started this project here at West Ham. Of course it is always important that you know they are supporting you.
"Nobody expected to lose the first four games but that will not change, at least in my mind. If the owners and Karren continue thinking the same way, that is always good news."
Marco Silva's Everton have recorded three draws and a win in their opening four league matches but will face West Ham without Brazilian forward Richarlison, who is serving the final game of a three-match suspension.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
Share
