The Brazilian sustained the injury in the first half of his side's 3-1 victory over Manchester United on Sunday.
"He'll be out for a month so that's a blow. It was a sad sight to see him walking off the pitch. He's frustrated because he was playing well on Sunday," said Liverpool's head of sports medicine and sports science Dr Peter Brukner on the club website.
Aurelio joins fellow defender Martin Kelly, who also has a torn hamstring, on the injury list ahead of their Europa League last-16 first leg clash with Braga on Thursday.
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