The Wales flanker injured his hamstring during the closing stages of the 16-15 second Test defeat to the Wallabies and remained in Melbourne after the match under the supervision of Lions team doctor Eanna Falvey.
Warburton underwent a full medical assessment and a scan confirmed a significant tear in his left hamstring.
The 24-year-old, who will remain with the tour party for the third Test in Sydney said: "It is incredibly disappointing to be ruled out of the tour through injury as we head to Sydney for the deciding match.
"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."
Meanwhile, the fifth edition of HSBC's Lions Weekly - a video round-up of news and views from the tour Down Under - features respected pundit Jonathan Davies interviewing Brian O'Driscoll the morning after the second Test.
O'Driscoll told HSBC's Lions Weekly: "We haven't played well yet, we've defended reasonably well, albeit we did let them in for a seven-pointer in the last few minutes but we've shown nothing.
"We have put phases together, we've been a bit blunt in our attack, we need to change all that if we're going to put in a performance that deserves a victory."
The Dubliner added: "I've made no secret of the fact that I badly want this, it's my fourth tour and I have tasted defeat three times. It's not easy.
"I understand the nuances of Lions tours now and this week in particular is a re-run of 2001 - you're down a little bit after the second Test but you can't afford to be down for long. You have to realise there is one more huge opportunity that lies ahead of you."
The first four episodes of 'HSBC's Lions Weekly' are still available via YouTube - www.youtube.com/LionsHSBC.