Scans on McMahon's right thigh earlier this week revealed a grade two tear in the affected area. Grade two is deemed as medium damage, with grade one being the mildest and grade three the worst.
Following the results of the scan, McMahon is expected to be sidelined for a total of 4-5 weeks.
Speaking about McMahon, Bantams boss Stuart McCall said: "He has been terrific for us since day one this season.
"It is obviously a big disappointment to lose him but we know that injuries are part and parcel of football sadly.
"We are probably looking at being without him for roughly a month. Tony is very determined to get back as soon as possible though, so hopefully we might get him back slightly quicker."
In need of a defensive pick-me-up following McMahon's recent injury, McCall could be about to receive a timely double boost in that area.
After being sidelined since the end of last season with a groin problem, Stephen Darby could be given the green light to get back involved with the rest of his team-mates as soon as the end of this week.
Fellow defender Matthew Kilgallon is even further ahead having trained fully with the squad since Monday.
The 32 year-old summer recruit has yet to feature for City so far after joining the Bantams late on in pre-season.
The centre half was put on his own fitness programme to get him back up to speed, although his progress was hampered slightly by a minor hamstring strain a couple of weeks ago.
McCall added: "Matt has been training with the rest of the lads this week. We'll just monitor him to see how he goes.
"He is desperate to play his part as soon as possible - he is feeling stronger each day.
"If we feel he has come through this week fine, then we will look at the possibility of getting him involved in some way either on Saturday (vs Oldham Athletic) or Stoke City (Checkatrade Trophy) next Tuesday."