The Spain Under-21 international went under the knife in Germany on Thursday and will return to the Spanish capital shortly
The promising attacker, 21, sustained the injury in the opening minutes of Madrid's 3-1 Champions League win over Schalke on Tuesday and will consequently be out of action for the remainder of the 2013-14 campaign.
"Jese Rodriguez has Thursday undergone surgery at the Hessingpark-Clinic in Augsburg at the hands of doctor Ulrich Boenisch, with Real Madrid club doctors Jesus Olmo and Francisco Morate supervising the operation," a statement on the club's official website reads.
"The successful surgery consisted of repairing the anterior cruciate ligament and the lateral meniscus of the player's right knee.
"The player will return to Madrid after he is dismissed from the hospital, which is expected in the upcoming days."
Jese had been one of the revelations of the 2013-14 campaign, scoring eight goals in 31 appearances in all competitions.