The 22-year-old, who has endured rotten luck with injuries this season, has made only four appearances after undergoing hip surgery back in August and then sustaining a knee injury.
The left-back was a substitute in the recent defeat at Gillingham and made his first start since the opening day in last Saturday's 4-1 win over MK Dons, but was withdrawn after an hour due to a calf injury. Leigh Bromby or Aidan White could return to the back four in Parker's absence.
Manager Simon Grayson must decide whether to recall Jermaine Beckford to his starting line-up after the leading goalscorer stepped off the bench to fire his 29th and 30th goals of the season last weekend, or stick with in-form pair Max Gradel and Luciano Becchio up front.
Bradley Johnson is hoping to keep his place in central midfield alongside Neil Kilkenny, but Jonathan Howson and Michael Doyle are both pushing for recalls.