The 21-year-old was unable to complete 90 minutes of a 2-1 Coppa Italia semi-final first-leg victory over Inter and medical examinations have today confirmed the extent of the damage.
A statement on the club's official website read: "Mattia Destro twisted his right ankle and left knee during the Coppa Italia semi-final first leg.
"The player underwent two rounds of tests which identified a tear to the lateral meniscus in his knee.
"He will therefore require an operation via arthroscopy, which will be performed by Professor Cerulli in Rome over the coming days."
The Italy international has scored four goals for the Giallorossi since arriving from Siena in a 11.5million euro deal in July.