Delph suffered the injury during a training session prior to Villa's win over Portsmouth on Sunday.
The 20-year-old now looks set to be sidelined for a considerable length of time, but as yet the club cannot confirm the full extent of the injury.
"Fabian is awaiting results from scans taken to determine the extent of a serious knee injury suffered in training on Saturday," said a club statement.
"The player had to be stretchered off and immediately underwent tests. Doctors will know what damage has been done in the next 24 to 48 hours."
The 20-year-old former Leeds United star joined Villa last summer, but he has failed to make the expected impact making just eight Premier League appearances.