Dyer, 21, appeared to get his studs caught in the turf and turned his ankle at Valley Parade.
Burton are awaiting the results of scans but Rowett is not expecting positive news.
"We've not had conclusive proof yet, but we're pretty sure he's damaged some ligament in his ankle," Rowett told the Burton Mail.
"How long he's out and how serious it is depends on which ligament it is and what he's done to it.
"Jack felt a click in his ankle and heard something, which suggests something snapped or tore."