The Lions captain suffered a hamstring injury with 13 minutes remaining in the second Test, with Warburton leaving the field with his side six points ahead before the Wallabies salvaged a slender 16-15 win in Melbourne.
Warburton missed the opening two matches of the Lions tour against the Barbarians and Western Force due to a knee injury, and Ireland’s Brian O’Driscoll will replace the Wales international as skipper for the decider.
And the 24-year-old, who helped the Red Dragon win the Six Nations Grand Slam crown this spring, backed his team-mates to beat the Wallabies in the final Test and seal a series win despite his absence.
“It is incredibly disappointing to be ruled out of the tour through injury,” Warburton said.
He added: “I wish the team all the best and hope I can play some part in the build-up this week. I am confident the boys can finish the job off and secure the series win.”
Warburton is likely to be replaced by Leinster flanker Sean O’Brien or his Wales team-mate Justin Tipuric at number seven for the final Test in Sydney.