And the All Blacks duo are also in line to miss the Rugby Championship that follows.
Crotty fractured his thumb in the semi-final win over the Hurricanes and had surgery on Sunday to stabilize it.
He will be sidelined for up to eight weeks.
Barrett will miss the next five to six weeks after fracturing the second metacarpal at the base of his index finger.
The Crusaders have ready-made replacements in the midfield and at lock.