Hanson picked up the injury during the warm-up before Tuesday's match at Milton Keynes Dons.
Parkinson had already ruled Hanson out of this Saturday's trip to Colchester United but the City chief now knows he will potentially be without the striker for the next four to five games after that following the results a scan on the injury.
Hanson's scan this Thursday afternoon revealed a slight tear in the thigh area.
Along with the suspended Alan Sheehan, Hanson now joins the injured trio of Andrew Davies, Lewis Clarkson and Matthew Dolan currently on the sidelines.
As a result of the injuries and Sheehan's suspension, apprentice defender James Pollard has joined fellow scholars Reece Webb-Foster, Sam Wright and James King - all of whom travelled to MK Dons - in City's squad for the Colchester match.