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The 24-year-old, who is also Wales captain, faces a race against time to be fit for his country's November internationals.
Warburton picked up the injury on the Lions' successful tour to Australia, suffering the tear in the latter stages of the second Test defeat in Melbourne.
And now the Blues' medical chief John Miles says he will need a lengthy recovery period.
"Sam suffered a grade three tear to his left hamstring in the second Lions Test against Australia on the 29th of June," he said.
"He has had a scan with specialists in London yesterday (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."
Warburton will miss the opening rounds of Celtic League matches as well as Cardiff's first two European Cup encounters.
The openside flanker could also miss Wales' November Tests against South Africa, Argentina, Tonga and Australia, depending on the length of his recovery process.
If it takes nearer 12 weeks, he could be available to coach Warren Gatland, but if he needs the full 16 weeks, he is like to miss all four Tests.
