The 30-year-old suffered the "slight fracture" during the Republic of Ireland's 1-1 draw with Germany in their Euro 2016 qualifier earlier this month.
In this afternoon's press conference, Hughes told reporters: "Glenn unfortunately has a fracture in his leg. He picked it up in the international game. There is a slight fracture, but he hasn't been put into a plaster cast.
"We feel that he can come back sooner by avoiding that. It is a blow for him and it is a blow for us because we are likely to be without him for four to six weeks. It is disappointing but thankfully we have options in there."
Whelan played no part in the Potters' 2-1 victory over Swansea City last weekend.