Hopes were abound late last week that Windass, who has endured an injury-hit campaign, would be in contention for the run-in, starting with Saturday's League One home match with Cheltenham Town at Hillsborough.
But the former Rangers player has broken down in training this week with a recurrence of hamstring trouble, depriving the Owls of a match-winner and potential trump card at a key juncture of the campaign.
Boss Moore said: "We had a little setback with Josh in the week in training. We are going to assess him and see over the next few days with the reports and what comes back with him.
"It is too early to say whether he will miss the rest of the season. We have taken him out of training and we will make an assessment of him in the next few days.
"He is absolutely gutted. He so wants to come back. When you see where we are and the season we have had to date, he wants to be part of it. He wants to contribute.
"He has been okay but he is so desperate to come back and play."
Wednesday will also be without another forward option in Saido Berahino for tomorrow's game, while Olamide Shodipo is expected to re-join the squad shortly having made a return to training earlier this month.
Windass joins defenders Lewis Gibson, Liam Palmer, Dennis Adeniran and Tyreece John-Jules in the treatment room.
On Shodipo, Moore added: "Midy is back now. We think he is back in there with us. I would like to give him another seven days and train some more. He will then be another attacking option for us on the left hand side. It is good that he has had this week to train."