The flanker, who struggled with fitness issues at the start of the tour, was forced off late on during the Lions' 16-15 defeat in the second Test on Saturday.
Warburton underwent a full medical assessment after the match where a scan confirmed that the Welshman has suffered a significant tear in his left hamstring.
"It is incredibly disappointing to be ruled out of the tour through injury as we head to Sydney for the deciding match," said Warburton.
"I wish the team all the best and hope I can play some part in the build up this week. I am confident that the boys can finish the job off and secure the series win."
Warburton will remain in Australia for the final match of the tour in Sydney on Saturday.