The 21-year-old was knocked to the ground and landed awkwardly when he tangled with Schalke defender Sead Kolasinac in the second minute at the Bernabeu and had to be replaced by Gareth Bale.
"He has had bad luck and everyone at Real Madrid has had bad luck because we will lose a young player who has been doing very well this season," coach Carlo Ancelotti told a news conference.
"But this is football and players suffer injuries at times during their careers. We are sad and it has affected us a lot but it could be a chance for him to build strength of character. We have to stay positive.
"We will help him through it and wait for him to come back next season." Real won 9-2 on aggregate, after a 3-1 home win in the second leg, to reach the Champions League quarter-finals.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Reporting by Iain Rogers, editing by Robert Woodward)
