Morris limped off towards the end of the first half of the Final Third Development fixture at the club's training ground on Tuesday afternoon after falling awkwardly under a Wrexham challenge.
The game was actually Morris' first in nearly three months after he originally injured his knee away at Fleetwood Town back in September.
Parkinson said: "It is really frustrating for ourselves and Josh.
"We could have possibly had the reserve game called off because conditions weren't great with the recent wet weather we'd had. But we pulled out all the stops to get it on because we wanted to give Josh a chance to play.
"Unfortunately, Josh has re-injured his knee in the game.
"He has seen our knee specialist Dr Steve Bollen, and Steve is happy that the knee is stable but there is a slight injury there.
"It is not as bad as before but Josh has to dust himself down now, get through his rehab, and get himself ready to return in a few weeks."
While Morris might be ruled for Sunday's Emirates FA Cup tie with Chesham United, Parkinson has revealed loanee defender Reece Burke is back in contention after recent injury and illness.
Parkinson said: "He's had a good week on the training pitch - he has trained well.
"He is definitely competing for a place in the side come Sunday."
Along with Burke, all of City's five loanee players - Kyel Reid, Jordan Bowery, Luke James and Lee Evans being the others - are eligible to play for City at the weekend.
James and Bowery's availability in particular should give Parkinson some food for thought as he ponders his attacking options for the Chesham tie.
Parkinson added: "We have a lot of options.
"There is competition for places all over the pitch, certainly up front.
"Billy (Clarke), Luke James, Devante Cole, James Hanson, Jordan Bowery - we have some good options.
"Any one of those five could justifiably say they have a case for starting on Sunday.
"Everyone wants to play because the FA Cup is a great competition but we have to make sure we pick the best starting eleven and bench for this tie."