Back-Row Warburton suffered the injury during the first half but continued to play on, only telling medical staff he had been hurt after he left the field.
Wales team physiotherapist Mark Davies, confirmed Warburton's injury;
"A scan after the game has revealed a fracture to Sam's jaw which will prevent him from playing for at least a four-week period.
"He picked up the injury in the first half but was able to continue to play a part in the game and actually made no mention of it himself until after the final whistle, later on a closer inspection has obviously revealed the full extent of the problem."
Warburton's fellow Blues player Andy Powell was also withdrawn from the squad last week after suffering a thigh injury in training. Ian Gough has now been called up to the squad as additional back row cover.