The defender was forced off against the Championship leaders just before half-time.
Scans have revealed that he has broken the second metatarsal in his left foot, meaning that the 23-year-old will miss Derby's remaining four games of the season.
McEveley joins three of his team-mates in being sidelined with similar injuries, and manager Nigel Clough told the club's official website: "It is a big blow to us as we are already short of defenders and Jay has been
playing extremely well since coming back into the team.
"We seem to be blighted by metatarsal injuries at the moment, with Jay joining Paul Green, Steve Davies and Miles Addison who are all out for the rest of the campaign.
"It means we will have to dig in as a squad and make the best of it. We have four matches remaining and it is imperative to get the points we need to secure our survival."