Morris damaged his medial ligament after taking an awkward tumble towards the end of the encounter with the Cod Army at Highbury Stadium.
Speaking to Bantams Player HD about Morris' injury, Parkinson says he is at least thankful that the problem isn't as bad as it could have been, and he knows that it does give another member of his squad the chance to impress now.
Parkinson said: "Josh finished the (Fleetwood) game which is a good sign.
"He has opened up his medial ligament but it is at least nowhere near as bad as the injury suffered by Billy Clarke.
"It is a set-back that we will be without Josh for probably three weeks, maybe four. He has been playing really well but it opens up a place for someone else within the squad.
"We have plenty of options to choose from. Throughout the course of the season, you have to accept that you will pick up injuries and we believe we have the strength in depth to deal with them."
In other news, Parkinson revealed that the club have an agreement in place with West Ham United to extend the loan deal of central defender Reece Burke by a further month.