The former Plymouth star missed the win at Norwich at the weekend with the problem which he picked up during Friday's training session.
Irishman Coughlan, perhaps Wednesday's most consistent performer this season, had a scan earlier today which revealed that he would miss a minimum of seven weeks.
Meanwhile, Wycombe striker Nathan Tyson admitted that he wanted a move to Wednesday, but he believes that the Hillsborough club got cold feet after seeing him have a poor game at Lincoln City.
He told the Ealing Times: "I felt that they didn't really want me there and that I wasn't the player they were looking for, I was flattered by their offer.
"The place was amazing, the fans are fantastic and it would have been lovely to go up there and play in a stadium like that in front of their fans but the vibes from the backroom staff and the manager weren't right."