The Brazilian superstar was stretchered off in tears toward the end of PSG's 3-0 victory over its great rival at the Parc des Princes, having innocuously rolled his right ankle and flopped to the ground in pain, AFP reported.
Paris coach Unai Emery said after the game that early examinations in the dressing room showed Neymar had twisted the ankle.
Le Parisien reported that the 26-year-old underwent tests at a hospital just outside Paris in the early hours of Monday which ruled out a "fracture or a serious sprain".
Speaking to French television after Sunday's match, PSG captain Thiago Silva said, "I'm not a doctor, but I don't think he'll be available on Wednesday (when PSG faces Marseille again in the French Cup). He has to rest."
Le Parisien suggested that the world's most expensive player will definitely miss Wednesday's French Cup match with Marseille as well as next Saturday's trip to Troyes in Ligue 1.
The Champions League last 16, second leg against Real at the Parc des Princes in Paris on March 6 is just over a week away, leaving Neymar little time to recover fitness.
"We will be optimistic. If I had to say today (whether or not he will face Real) I would rather say yes to being optimistic," said Emery on Sunday night.
Meanwhile, Real coach Zinedine Zidane said he takes no satisfaction from the injury that threatens to rule Neymar out of next week's tie between the Spanish club and PSG.
Zidane said on Monday, "I'm not happy with the Neymar injury and I hope he can be back for the game. I will never want a rival player to be out injured."
PSG is 14 points clear of Monaco at the top of Ligue 1 after Sunday's game, but the Champions League is crucial to the French club and the French giant lost 3-1 in Madrid in the first leg two weeks ago.