The Barcelona striker was taken to hospital after being injured in the closing stages of the 2-1 quarter-final win over Colombia that kept the hosts on course for a sixth title.
Neymar, who has scored four goals in the tournament, went down after a challenge by Colombia's Juan Zuniga in the 88th minute and looked to be in some pain.
He had to be carried off on a stretcher and was replaced by defender Henrique.
Boss Luiz Felipe Scolari had initially said: "Neymar was kneed in the the lower back and was in a lot of pain. I don't know if he will be able to play the next game.
"It won’t be easy for him to recover, based on what the doctor told us and the pain he’s in."
The 22-year-old was in tears after taking a knee to the back from Zuniga and Brazil doctor Rodrigo Lasmar later confirmed he had sustained a fractured vertebra that would end his World Cup.
"It's not serious in the sense that it doesn't need surgery, but he'll need to immobilise it to recover," Lasmar said. "Unfortunately, he's not going to be able to play."
A subsequent statement from the Brazilian football confederation said Neymar was likely to be out for around a month, meaning the final on July 13 - should Brazil get there - would come much too soon.
"Neymar is out of the World Cup," the statement read. "The player suffered a fracture of the third vertebra and will not be able to recover in time to compete in the remaining two games of the World Cup - the recovery time predicted by the Brazilian team's medical department is four weeks."
Zuniga insisted he was "playing for the shirt from my country, not with the intent to injure", but Neymar was crying in pain as he left the stadium.
His absence will be a huge blow to Brazil, who will also be missing suspended captain Thiago Silva for the semi-final in Belo Horizonte.
The ref decided the game. Brazil should have finished with 8 yellows and 2 reds. Colombia should have finished with 4 yellows and 1 red (the foul on Neymar with only 10 mins left). Now that Neymar knows how it feels to get fouled and hurt, maybe he will stop diving around and play acting more than any other player on earth. On a side note, Neymar is the best diver i have ever seen. He actually convinces you he was fouled even though he wasn't, even in slow motion. Crazy.- soul controller