The injury only came to light when the South African flanker saw a specialist on Monday. He is expected to be out of action until January.
Although they have lost the services of Stander in the meantime, Munster have been able to promote another back rower, James Coughlan, to their Heineken Cup squad.
The Corkman, who turns 32 on Thursday, has been added to their European panel as permitted under the competition rules.
He had been omitted from the province's original squad after suffering a torn groin against Ulster in September. At that time, the prognosis was for a five-month recovery period.
However, Coughlan was particularly diligent about his rehab and made a successful return as a starter in the bonus point triumph over Glasgow.
Ivan Dineen, who was registered in place of Coughlan back in September, has now made way for the fit-again number 8 as per Heineken Cup rules.