Borini first sustained an injury to his foot in the Reds' 2-1 home defeat by Manchester United on 23 September, Liverpool said in a statement on their website.
The club said the 21-year-old then "aggravated the problem resulting in a fracture" when on international duty with Italy's U-21s ahead of their game against Sweden on Friday.
"Typically, an injury of this nature requires a three-month rehabilitation period," the statement added.
Borini, who joined Liverpool from Roma during the close season, has scored just once in 11 appearances for the English Premier League side.
His absence leaves the club with just one recognised striker in Uruguayan Luis Suarez.