Shanahan said the injury is a high-ankle sprain that will keep the third-year player out for a while.
"He's going to end up going on IR here," Shanahan said on the "Tolbert, Krueger and Brooks" show.
Jones' injury occurred on Sunday against the New Orleans Saints. It's a difficult loss for a defensive front that has already lost Ronald Blair (ACL) and Damontre Moore (fractured arm) to season-ending injuries.
"We've got guys who can come in and step it up," Shanahan added. "Jullian (Taylor), who has been hurt, probably won't be able to play this week but we expect to get him back, hopefully, next week, if not the week after. He's going to have to step it up for us here with losing D.J."
The 49ers made Jones a sixth-round selection out of Ole Miss in 2017. He registered 23 combined tackles, two sacks, and a forced fumble through 11 starts this season. Jones has recorded 50 combined tackles, two sacks, a pass defensed, and a forced fumble through his three NFL seasons.
The 49ers will likely activate defensive lineman Kentavius Street for Sunday's game against the Atlanta Falcons. He has yet to play in a regular-season game after landing on injured reserve last year, his rookie season, and then again on September 1 this year after undergoing arthroscopic surgery on his knee.
"Plan on probably getting Kentavius Street up this week so we can have some numbers up there," Shanahan added. "Kentavius is a guy we spent a fourth-round draft pick on, who's battled some injuries, and he's just getting there, ready to play. With this injury [to Jones], he's going to get an opportunity.
"It's a big loss, but we've got some other guys in here, and we've had to do this at some other positions this year. It's part of the NFL. This is what happens, and injuries change a lot of stuff, and that's why you've got to have a deep team."
You can listen to the entire conversation with Shanahan below.
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