McArdle missed both of City's home games this week after dislocating his left shoulder towards the end of City's goalless draw at Bury last weekend.
Following a visit by McArdle to a specialist on Friday to check over the injury, City have now been told to expect the defender to be out of action for the next month.
The City chief also revealed that McArdle is likely to need surgery after the end of the season to ensure the area is totally problem-free going forward.
Parkinson said: "Rory is going to be out for another four weeks.
"The specialist feels he will probably need an operation in the summer as well.
"Hopefully in four weeks the rehab Rory has to do will allow him to continue the season.
"Rory is an important player for us so we hope he can finish the season off with us before going into the summer and completely rectifying the problem."