Sam Warburton stayed in Melbourne, after Saturday's defeat against the Wallabies, to undergo a scan on his leg.
The Lions have now confirmed that he suffered a 'significant tear in his left hamstring.'
He will remain with the tour party, but will not play in the final test.
Warburton 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."
More top news
It'll be an unsettled afternoon across Wales, with blustery winds and heavy rain. Gales expected in many areas.
A bronze war memorial which was moved from a fire damaged chapel in Aberystwyth seven years ago is now being returned to its original place.
The compulsory 'scores on the doors' system is helping to drive up standards across Wales, according to the Deputy Health Minister.