The highly-rated 21-year-old went down in agony under a challenge from Sead Kolasinac just two minutes into the second leg of Real's UEFA Champions League last 16 tie at the Bernabeu on Tuesday.
Jese managed to get to his feet, but was replaced by Gareth Bale six minutes later and was sent to hospital for tests.
The La Liga leaders revealed following their 3-1 victory - which sealed a 9-2 aggregate success - that Jese has sustained a tear to the anterior cruciate ligament in his right knee that looks set to cut short his season and could end his hopes of forcing his way into Spain's FIFA World Cup squad.
A statement on the club's official website said: "After scanning and imaging tests conducted at the Hospital Sanitas La Moral, our player Jesse Rodriguez has been diagnosed with a complete tear of the anterior cruciate ligament in his right knee."
Jese's injury comes just five days before the El Clasico clash with champions Barcelona and he is not expected to play any further part in Real's attempt to secure a famous treble.
