The Brazil forward was taken off during his country's 2-1 win over Colombia after suffering a fractured vertebra following a heavy challenge from Juan Zuniga.
He will now miss the rest of a competition, with captain Thiago Silva also ruled out of their semi-final against Germany due to suspension.
Barcelona man Neymar recorded a video message which was played in Brazil's press conference in which he vowed to make a swift return and stated his dream of becoming a World Cup winner.
"Brazilian people - players, coaches and fans - this is a very tough moment. It's hard to express my thoughts in words," the 22-year-old said.
"I want to tell you that I'll be back to the field as soon as possible. I would like to thank you for your support and affection expressed through the messages that have been sent to me.
"My dream has not ended yet, it was suspended due to a move, but it is still alive. I am sure my partners (team-mates) will make sure I can achieve my dream, which is to be a champion.
"Another dream of mine was to play on a World Cup final, but I won't be able to do it now. Although I'm sure that my partners will win and be champions along with me, and we, Brazilian people, will be celebrating this achievement.
"Thank you all!"
Following the game, Zuniga stressed he had not intended to hurt Neymar and that it had simply been a "normal move".
A day later, he added his apologies for causing the injury and wished the Brazilian a quick recovery.
"I'm profoundly sorry for the saddening injury that Neymar suffered in the match between Brazil and Colombia," he wrote in a statement published via his Instagram account.
"Although I feel that this action is normal throughout the course of the game and there was no malice, ill intent or negligence on my part, I want to send a special message to Neymar.
"I admire you, respect you and consider you one of the best players in the world.
"I wish you a speedy recovery, that you come back soon to fill reignite the footballing world with your talent and skill that, without a doubt, has been the most I've seen in all my 12 years as a professional footballer.
"To the Brazil fans, who has seen one of their player, an exemplary person, ruled out of the World Cup, I send a special message and thank you for all of the support you've shown the Colombian national team in every single match we've played."
