Family loyalties will be placed to one side as Latics search for points to preserve their npower League One status, while Johnson Snr is chasing automatic promotion with the Glovers.
Wesolowski was absent as his team-mates battled to a vital 1-0 win over Greater Manchester neighbours Bury at the weekend due to a slight tear to his medial knee ligament.
The midfielder has undergone a painkilling injection and, although Tuesday night comes too soon, he may play again this term.
Johnson told Oldham's official website: "James won't be ready for Tuesday, but possibly could be for Saturday or he could be out for the season. We will have to see how it settles."
Norwich loanee Korey Smith has extended his spell until the end of the campaign and is expected to continue in central midfield in Wesolowski's absence.
Experienced defender Cliff Byrne should be fit once more following a groin problem, but young striker Dan Taylor (knee) will not play again this season.