The news will come as a huge blow to PSG as they have it all to do in the second leg having lost at the Bernabeu 3-1.
The Brazilian, who signed for PSG in a world-record move from Barcelona a year ago, is now a serious injury doubt for the match against Real Madrid. "I think there is a small chance for him to be ready for the match".
The 26-year-old captained Brazil to their first ever Olympic gold medal 18 months ago on home soil and is seen as crucial to their hopes in Russian Federation in June and July.
Neymar has been a roaring success in Paris since joining in world-record transfer last summer, scoring 29 goals in just 30 appearances for PSG. However, now while the Brazilian has been at his best, PSG will have to play the better part of a month without Neymar as the 26-year-old has picked up an ankle injury.
The Parisians were hoping to make the most of their home field advantage, and on Neymar, who has scored 28 goals in all competitions all season.
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It hasn't been made clear when will Neymar return to full fitness.
But Emery has provided a welcome injury boost for the French giants, claiming Neymar could yet be fit to face Los Blancos.
The player is expected to miss quite a big part of what's left of the season, as he's only set to get back to training in late April.
With the World Cup on the cards, Neymar shouldn't be rushed into action.
The Spanish team's coach, Zinedine Zidane, comment on Neymar's injury, saying: "I don't like it when a player hurts himself, I am not happy about the injury".