Jones' injury took place during Sunday's win over the New Orleans Saints. The team is awaiting the results of further testing.
Shanahan didn't sound too optimistic about Jones' status and said the loss could prompt the 49ers to activate defensive lineman Kentavius Street from injured reserve.
"We've got Sheldon (Day), who can do it," Shanahan added, "we've got Solomon (Thomas), who can do it, all the guys on the inside, who can do it, (Arik) Armstead, [DeForest Buckner]."
The other players who will sit out Wednesday's practice are defensive end Dee Ford (hamstring), safety Jaquiski Tartt (ribs), defensive lineman Jullian Taylor (elbow), and cornerback Richard Sherman (hamstring) and K'Waun Williams (concussion).
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