McMahon missed last Saturday's trip to Barnsley due to illness but Parkinson has revealed that the 29 year-old has been bothered with the bug since the start of the season.
After undergoing some tests, McMahon has been ordered to rest up, meaning he will once again be unavailable to City when Port Vale visit the Coral Windows Stadium this weekend.
Frenchman Christopher Routis is also likely to miss out again due to a recent hamstring problem.
Parkinson said: "He'd (Tony McMahon) had a good pre-season with us but then he picked up this virus before the first week of the season.
"He hasn't felt himself by a long way since then.
"It flared up again before the weekend so we've sent him to see a specialist this week.
"He's had some blood tests and there is some concern about a virus in his system so he needs a period of rest.
"We are pleased that we've found out what it is but still disappointed to lose him for action at the moment.
"Once he's got over this problem though, we're confident he'll come back stronger than ever."