The former Roma striker had to be substituted at halftime after sustaining the injury during the Reds' recent 2-1 defeat to Manchester United and further aggravated the blow while on international duty with Italy.
And the club has now confirmed that the 21-year-old will go under the knife after being assessed at Melwood and is set to be absent for some time.
The blow leaves Liverpool with just one senior striker, Luis Suarez, available following its failure to capture Clint Dempsey from Fulham during the summer transfer window.
Youngsters Samed Yesil and Jerome Sinclair have both recently featured in the League Cup and could now be handed further opportunities.
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