Wootton, 21, who had a loan spell at Posh last season and a month ago returned for a second stint with Darren Ferguson's side, sustained the injury in training last week and is expected to be out for around six weeks.
"It's a blow for Scott and a blow for the team," said London Road boss Ferguson. "But we have him on loan until the end of the season so he could still come back.
"We have plenty of cover at centre-back. Gaby Zakuani played very well there at the weekend and Shaun Brisley has also performed well there. Michael Bostwick has been very good at the back and we also have Craig Alcock."