The 28-year-old defender also faced death threats on social media for the incident when his knee clattered into the striker's lower back at the end of Brazil's 2-1 defeat of Colombia on Friday.
Neymar will miss the rest of the tournament and the whole of Brazil seems to have been traumatized, with even football legend Pele declaring "it hurts our hearts".
"The FIFA Disciplinary Committee is analysing all the elements provided, the videos and the match reports, and will decide whether or not to take action," FIFA spokeswoman Delia Fischer told a briefing.
Zuniga, who plays for Napoli in Italy, has denied he intentionally sought to injure the 22-year-old Brazilian.
"When I'm on the field I always do what I have to, to defend my country and the shirt I wear, but always without intent to injure anybody," Zuniga told Brazilian television after the game.
The Colombian said both sides were playing to their limits.
"It got a bit heated. There were strong tackles but the Brazilians were doing the same. It's normal. I didn't make that challenge trying to break his spine. I was defending my country.
"It's a very sad thing. I hope, with the help of God that it's not too serious because everyone knows he's a great talent for Brazil."
Brazilian newspapers urged the national team -- who now play Germany in the semi-finals -- to win the World Cup for Neymar, while some assailed his Colombian opponent who also became a social media target.
Some internet death threats were made while the less offensive posts called Zuniga a "monster" and the "biggest villain in the history of football".
Brazil football legend Pele said the whole country was heartbroken by the injury.
"It hurts our hearts to know that he can no longer defend Brazil in the World Cup," said Pele on Twitter.
"I was also injured during the 1962 World Cup in Chile, and I was out for the rest of the tournament," he wrote. "But God helped Brazil continue on to win the championship. I hope the same will happen with our Selecao in this World Cup."
Brazil will face Germany in the semi-finals on Tuesday.
Brazil won their first World Cup in 1958 and four years later Pele was injured in the second game against Czechoslovakia. They won the final thanks to the dribbling skills of another legend, Garrincha.
Former World Cup winners Ronaldo of Brazil and Italy's Fabio Cannavaro appeared at the daily FIFA briefing where the spokesman announced the disciplinary inquiry and Neymar's injury dominated debate.
"The injury was very violent," said Ronaldo. "I believe there was an intention to hurt by the player. I believe it was very aggressive and very violent."
"I believe that it was a situation which could have been avoided," he said.
"I didn't like that very high knee. That leads me to believe it was a foul with a prior intention to cause harm. It didn't give me a very good impression. It's a very evident foul," the Italian added.