The Brazil international suffered the injury in the opening minutes of Sunday's Barclays Premier League draw with Manchester City at Anfield.
It is a fresh blow for the 25-year-old, who had won his place back in the side after missing most of last season following knee surgery.
Rodgers said: "It is very unfortunate. He has worked ever so hard to come back and he has been an outstanding player for me and person off the field as well.
"The indications are two to three months. It is quite a unique injury at the top of his right thigh.
"He has had a scan and we will see a specialist this evening [Wednesday]. We'll see if it needs an operation or whether it is just recuperation."
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