Fletcher, who has notched five goals in his last six appearances, is struggling to overcome a groin problem he suffered in the Owls' 4-2 win over Blackburn Rovers before the international break.
Steve Bruce, the Wednesday manager, told The Star: "I don't think Fletch will make it.
"It is a blow to us as Fletch has been playing very well. But that is football and we have to get on with it.
"Let's hope someone else can step up to the mark."
Fletcher capped his 100th Owls outing in style against Rovers, tapping in the opener from close range after good play by Dominic Iorfa. The 32-year-old was withdrawn just before the hour mark and replaced by Atdhe Nuhiu.
Although Fletcher's injury is a setback the Owls could have done without in their pursuit of a top-six finish, Bruce has other attacking options at his disposal. Fernando Forestieri, Lucas Joao and Gary Hooper are in line to be included in the matchday squad for the trip to the bet365 Stadium, having returned to full training.
It promises to be a tricky selection for Bruce as Forestieri and Joao have not featured in a number of weeks due to injury while Hooper has not played a competitive match since Boxing Day 2017.
"Forestieri, Joao and Hooper all trained on Tuesday so that is good news," said Bruce. "They are okay at the moment.
"Whether they are ready (to start) or not is another matter."