Witherspoon, 24, exited Sunday's 24-20 win over the Pittsburgh Steelers in the fourth quarter and was replaced by Jason Verrett, who was later replaced by Emmanuel Moseley.
Witherspoon was seen in a walking boot after the game and underwent an MRI on Monday morning to determine the severity of the injury.
"I felt real bad for him because he's been playing at a high level," Shanahan said. "He's been covering very well. He's been playing very physical, too. I thought yesterday was probably his most physical game I've seen him have. He was making tackles, throwing his body around, and he's been covering very well all year.
"It is unfortunate for him, but these setbacks do happen in this league. It's part of football, and he'll work to get back. And when he comes back, we expect him to be right where he was when he left."
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Shanahan said Moseley is the leading candidate right now to start in place of Witherspoon, but there will be a competition with Verrett and others. The coach also didn't rule out the possibility of looking outside the current roster for some cornerback help, if a move makes sense.
"We've got D.J. Reed, who can play corner," Shanahan said. "We've got [Moseley], and we've also got Verrett. We've got three guys that can do it. We know Jimmie (Ward) can also play corner so we've got other guys on this team who can play. So it will be next man up."
The 49ers made Witherspoon a third-round selection out of Colorado in 2017. He has registered nine combined tackles, five passes defensed, an interception, and a touchdown through three starts with San Francisco this year.
Witherspoon has recorded 78 combined tackles, 16 passes defensed, three interceptions, a touchdown, and a forced fumble through his three NFL seasons.