Morsy received his 10th yellow card of the season during the Valiants' 2-0 defeat to Bristol Rovers on Tuesday night and the midfielder must serve a two-match ban.
He joins skipper Doug Loft, who will complete a three-match suspension at Bootham Crescent, and defenders Darren Purse (calf) and Dan Jones (knee) on the sidelines.
Also absent will be Ashley Vincent after he was carried off on a stretcher at the Memorial Stadium in midweek.
Vale are still waiting to discover the full extent of Vincent's injury but the winger is not thought to have broken his leg as initially feared.
Meanwhile, it remains to be seen whether Ryan Burge will be involved. The midfielder faces disciplinary action from the club after failing to attend Vale's pre-match meal in Bristol and then breaking the club's social media guidelines after being omitted from the squad.