The on-loan Roma forward pulled up during Sunday's 4-2 defeat to his parent club, with medical staff confirming the extent of the damage on Tuesday.
A statement on genoacfc.it read: "Examinations conducted at the Baluardo Institute have discovered a sprain to Marco Borriello's right ankle.
"The striker has undergone both an MRI scan and an ultrasound.
"The medical staff estimate that he will be able to return to athletic activities in 45 days."
Borriello has scored three goals in seven appearances since returning to the Stadio Luigi Ferraris in August.