Asamoah sustained an injury in Juve's 2-0 win at Empoli on November 1, but played against Olympiacos three days later.
Juve initially expected the 25-year-old to be out for just over two weeks, but the Serie A champions confirmed on Tuesday that the Ghanaian has gone under the knife and will be out until March at the earliest.
"Kwadwo Asamoah was in Barcelona to undergo arthroscopic surgery designed to fix torn cartilage in his left knee," a Juve statement read.
"Operated on by Dr Cugat and accompanied by club doctor Causarano, the Ghanaian is expected to return to competitive action within three to four months."
Juve also announced that Brazilian midfielder Romulo, who is on loan from Verona, is to have an operation on an injured abductor muscle.
"The player is to be supervised by medical staff from his parent club, who will remain in constant contact with Bianconeri doctors," the club added.