Subsequent investigation showed he has sustained a fracture at the base of his thumb which will require surgery to repair.
He will undergo surgery today, and his return to play timeframe will be clearer after this procedure.
The Crusaders will advise an injury replacement for Cullen when this detail is confirmed.
The former New Zealand Under 20s flanker has had a stand-out rookie Super Rugby season and was sitting third on the most tackles chart in Investec Super Rugby Aotearoa, behind Hoskins Sotutu and Dalton Papali'i from the Blues.