Cripps, who has been back training with his teammates for the past month, felt discomfort in his back on Wednesday.
Scans later revealed the extent of the injury, which will keep him grounded for up to 12 weeks.
“Unfortunately this pre-season setback means Patrick will be out of action for up to 12 weeks,” Carlton Head of Football Andrew McKay said.
“While the news is disappointing, the positive is we have diagnosed the condition early, minimising his time on the sidelines.
“Given his professionalism and determination, we are confident Patrick will be ready for the 2017 pre-season competition.”