The in-form performer - arguably one of City's more influential players in recent weeks - was forced off only 18 minutes into the Gills contest at the weekend after failing awkwardly early into the match.
Morais went for an x-ray after the game to confirm that, thankfully, nothing was broken but Bantams medical staff will still need to check on the progress of the former Stevenage man before knowing exactly how long he'll be sidelined for.
Bantams boss Phil Parkinson said: "The checks have revealed that nothing is broken but he has damaged ligaments in his shoulder. It is a set back for Fil, especially the way he has been playing lately.
"We'll wait for the swelling to go down before getting a better idea of how long he'll miss.
"We picked up a few other knocks during the (Gillingham) game - nothing major - but we'll monitor those as well."