The 20-year-old has been a regular in the Lilywhites' defence this season following his summer transfer from Crewe.
He started the loss to the Iron at Deepdale, but had to be replaced after 21 minutes.
Manager Alan Irvine confirmed: "Billy's got a hernia (problem). He had it before the Southampton game but played through the 90 minutes and did very well and deserves an awful lot of credit for that.
"He'll be undergoing surgery in the new year and, hopefully, we'll be able to get him some treatment between now and the weekend so that he can be fit to play against Cardiff.
"We're obviously badly stretched as far as defenders are concerned and so we have to try and nurse Billy through this particular period."