Warburton sustained the problem in the second Test against Australia in Melbourne – won 16-15 by the hosts to level the series.
The flanker subsequently missed the triumphant third Test and his club, Cardiff Blues, have now confirmed he will be out until November.
"Sam suffered a grade three tear to his left hamstring in the second Lions test against Australia on the 29th of June,” said the club’s medical head John Miles.
"He has had a scan with specialists in London on Thursday which has shown the injury is already healing.
"He therefore does not need surgery but will require a period of rehabilitation between 12 to 16 weeks from the date of the injury.
"His rehabilitation will focus on range of motion, flexibility and specific strengthening of the hamstring in order for him to return to full health."