McMahon reported the injury following the 2-1 home win over Doncaster Rovers last weekend.
Along with McMahon, Josh Cullen will also need to be assessed ahead of City's match at the DW Stadium.
The midfielder picked up a tight calf while playing for West Ham United's Development Squad in their semi-final extra time win over Liverpool in the Barclays Under 21 Premier League Cup on Wednesday.
Cullen was able to play in the tie as part of the loan agreement between West Ham and the Bantams.
Parkinson confirmed: "We have Josh and Tony who are doubts for the weekend.
"We probably won't know until very close to kick off if they will be available for selection.
"We have players waiting eagerly for their opportunity if those two don't make it though.
"We had a reserve game this week, coincidentally against Wigan as well. There were players in our side that day (Tuesday) who were trying to show me they were ready to get back in the team.
"We played Port Vale's reserves a couple of weeks ago, (Jamie) Proctor and (Billy) Clarke featured in that game and they showed me that they were keen to get back in the side.
"Using one of the starters from the Wigan game - Josh Morris - as an example, he could be another player, like Proctor, who goes from not being on the bench to coming into the starting eleven and making a big impact."