The Wales international sustained the injury while playing in the third-place playoff in the World Club 10s in Singapore at the weekend.
A statement on the club's website said: "He underwent an operation on Monday to stabilise a fracture and is currently recovering in hospital in Singapore. The family of Owen Williams are now at his bedside along with senior Blues management and medical staff.
"Arrangements are currently being made to co-ordinate his safe transfer home at an appropriate time. Cardiff Blues and the Williams family would like to thank the many hundreds of well-wishers who have offered messages of support."