The Italian Football Association confirmed that the striker has suffered the injury while on international duty last week.
Having assessed the problem, the Reds have now revealed that surgery is required.
"The forward originally sustained an injury to the area during the recent Anfield clash with Manchester United," read a statement on the club's official website.
"He then further aggravated the problem resulting in a fracture and returned from international duty with Italy last week.
"Borini was assessed by the club's medical team upon his return to Melwood and a decision was made for the 21-year-old to have surgery."
The former Roma frontman is not expected to return until late January.