Wesolowski pulled up in training on Saturday and was left out of the squad which drew 1-1 at home to Walsall on Tuesday night.
Manager Paul Dickov had been hopeful the player would be fit for a quick return to first-team action, but the injury has turned out to be worse than the club initially thought.
The Australian had made a confident start to the season, crossing for Jordan Slew to score the Latics' first goal of the season in the 4-2 Capital One Cup defeat to Sheffield Wednesday, and the news will be a huge blow for the Boundary Park club.
Dickov told the Oldham Chronicle: "It is a massive blow for us.
"Anyone who has seen the last two games will know we have missed him."