But the Wales flanker should be fit to take his place in the Lions squad if he is named on April 17, Cardiff Blues coach Danny Wilson added.
"Sam has a low grade medial strain which will put him out for approximately six weeks, which won't interfere with the Lions," said Wilson.
"You see players who get back quickly if they follow religiously the protocol and they get a bit of luck.
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"And I am sure that will be the case with Sam in terms of him following the protocol, and then we will see, all being well, how quickly he can come back. 'Low grade' was the important bit of news," he said.
Warburton suffered the injury in Blues' 24-24 draw with Ulster on Friday. He hobbled off and the damage was subsequently revealed by a scan.
Warburton, who has won 74 caps for Wales and skippered the Lions in Australia in 2013, has impressed for club and country this season and has been tipped by four-times Lions coach Sir Ian McGeechan to lead the side again in New Zealand.
Although any injury is unfortunate, a period of rest could work in his favour ahead of the first game on June 3 against New Zealand Provincial Barbarians, after an arduous season with Cardiff and Wales.
The first test of three is on June 24.
(Reporting by Neil Robinson; editing by Richard Lough)
