The 28-year-old has been struggling with a hamstring injury he picked up while on international duty with Cote d'Ivoire and, thus, missed the Swans' English topflight encounters against Huddersfield and Leicester City.
Manager Paul Clement has confirmed the former Manchester City marksman will not be fit enough for the tie, alongside teammate Renato Sanches.
“Wilfried will not be fit,” Clement told club website.
“Renato came off against Leicester with an injury to his thigh.
“It is not the same one that he had while he was the national team [earlier this month], but it will keep him out of this game and possibly at the weekend as well.”
Bony has made just appearances since his switch from the Citizens. And Swansea will be hoping to defy all odds against the Red Devils to book a place in the quarter-finals of the English League Cup.