The midfielder was stretchered off after his knee gave way during Easter Monday's 3-2 victory over Oxford.
Morris, 23, subsequently went to hospital where his dislocated kneecap was confirmed.
The Welshman is now back in Cardiff receiving treatment and awaiting a further MRI scan. No date for his scheduled comeback has yet been set.
The Shots, currently second from bottom in League Two but just two two points from safety, are not in action this weekend due to scheduled opponents Southend taking part in the Johnstone's Paint Trophy final at Wembley.