The Italian suffered the injury on international duty in training, and leaves Brendan Rodgers with a striker crisis with Luis Suarez the only fit first-team forward
The Italian was due to play Sweden on Friday in the Under-21 Championships but an MRI scan revealed the injury, according to the Italian football association.
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Manager Brendan Rodgers is now likely to rely on youngsters such as Adam Morgan and Samed Yesil to step up to the fore during Borini's rehabilitation.
It also leaves Italy's Under-21 manager Devis Mangia with a headache as he now has to patch up his side as they go into their double header with Sweden.
The two-legged tie concludes next week, with the winner booking their place in the 2013 European Championship in Israel.
At his disposal now are strikers Giuseppe De Luca of Atalanta, Manolo Gabbiadini of Bologna, Ciro Immobile of Genoa and Samuele Longo of Espanyol.
The injury comes days after Borini called for "the utmost concentration" over both legs as the Under-21 side beat Belarus 2-0 in the first leg, only to beaten 3-0 in the return fixture in 2010.