The injury forced the forward's early return from international duty with Italy Under-21s last week, as he aggravated a problem first suffered in the recent 2-1 defeat to Manchester United.
Borini was replaced by young Spaniard Suso at half-time during that game but still joined up with his national team, only to damage the bone further in training ahead of the European Championship qualifier against Sweden. Italy won the tie 4-2 on aggregate.
A statement on Liverpool's official website read: "Borini was assessed by the club's medical team upon his return to Melwood (training ground) and a decision was made for the 21-year-old to have surgery.
"Typically, an injury of this nature requires a three-month rehabilitation period."
Borini has yet to score in five Premier League games since his summer move from Roma, with his only goal coming in Europa League qualifying against Belarussian side Gomel.
However, his absence means Liverpool have just the one recognised striker - Uruguayan Luis Suarez - until the January transfer window.
The Anfield club, who let England striker Andy Carroll go out on loan to West Ham United, have endured one of their worst starts to a top flight season, winning just one of their opening seven league matches.