"It is incredibly disappointing to be ruled out of the tour through injury," the 24-year-old said.
Warburton at a glance
5 October, 1988
Led Wales to Six Nations glory in 2012, then was restored as captain for the deciding victory against England in March that secured this year's title. Suffered disappointment in the 2011 World Cup when he was sent off in the 18th minute of the semi-final defeat against France
If selected, Brian O'Driscoll is likely to captain the side in what would be his ninth and final Lions Test.
Either Ireland's Sean O'Brien or fellow Welshman Justin Tipuric is likely to replace Warburton in the starting XV.
Despite the strength in depth they have at open-side, it is a major blow to the Lions' chance of a first series win in 16 years.
Warburton, who will remain with the squad for the rest of the tour, played a key role in the Lions gaining ascendancy at the breakdown in Saturday's second Test defeat in Melbourne.
Head coach Warren Gatland acknowledged the impact of his captain's departure 13 minutes from time, leaving him without a specialist open-side with O'Brien already on at number eight.
"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," said Warburton, who also missed the first two matches with a knee injury.
Gatland will now need to consider the balance of his back row for the finale, among a host of other selection decisions.
Australia v Lions: Warren Gatland blames 'critical turnovers'
The combination of Dan Lydiate and Warburton worked well in Melbourne and Tipuric would be the most direct replacement as the other specialist open-side in the squad.
But O'Brien, more of a ball-carrier than a breakdown forager in the Warburton mould, also offers a potent option.
Gatland is also weighing up potential changes at loose-head prop, where Alex Corbisiero is likely to return after a calf strain, at scrum-half with Mike Phillips fit again, and at centre, where Jamie Roberts - if he proves his recovery from a hamstring injury - and Manu Tuilagi offer alternative options.
The positions of hooker, lock and number eight could also come under scrutiny as Gatland and his coaches contemplate the side they will send out with the task of winning a first Lions series since 1997.
O'Driscoll, 34, has led the Lions on seven previous occasions, but only once before in a Test - the
infamous opener in New Zealand in 2005
when his involvement controversially ended inside the first minute after a double spear tackle.
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