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."
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The area came fourth behind Peru, New Zealand and Portugal.
A charity match is to be held later tonight to raise funds for a former Cardiff Devils player with a terminal neurological condition.
Staying rather cloudy for much of the day in the south, perhaps with a little rain at first.