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).
Related News
More San Francisco 49ers News
-
Five High-Value Vets the 49ers Could Secure in Free Agency
The time between the end of every football season and the first day of the NFL Draft is hardly as exciting as the seasons themselves. But it's a time of important work and after a dismal eighteen weeks and falling well short of a playoff berth, the 49ers have plenty of that... -
How the 49ers are aiming to keep Robert Saleh beyond one season
The biggest concern surrounding the San Francisco 49ers' reunion with Robert Saleh is the possibility of him becoming the team's third consecutive one-and-done defensive coordinator. Constant turnover in leadership has disrupted continuity on the defensive side of the... -
Watch 49ers' George Kittle, Kyle Juszczyk score in Pro Bowl flag football game
Tight end George Kittle and fullback Kyle Juszczyk were among four San Francisco 49ers players who participated in Sunday's Pro Bowl seven-on-seven flag football game in Orlando, Florida. The NFC squad defeated the AFC 76-63 in the high-scoring matchup. Juszczyk was the first... -
Jerry Rice offers warning to 49ers regarding Brock Purdy's contract
San Francisco 49ers quarterback Brock Purdy is poised for a massive payday this offseason, and he is likely to become one of the NFL's highest-paid players. The real question is where he will rank among the top-paid quarterbacks and how the structure of his contract will impact...