The Colombia defender said he didn't intend to injure the 22-year-old — who will be out for the remainder of the World Cup and for the next four weeks — during Brazil's 2-1 quarter-final win on Friday. Neymar was taken off on a stretcher in the 88th minute.
The FIFA disciplinary investigation is looking into the incident.
"I deeply regret the sad injury that Neymar suffered during the match between Brazil and Colombia," he told the BBC.
"Although I feel that these situations are a normal part of the game, there was no intent to injure, malice nor negligence on my part.
"I want to reach out to Neymar, who I admire, respect and consider one of the best players in the world.
"I hope you recover quickly and return to the game soon, so we can all support a sport full of the virtues and qualities that I've tried to follow in my 12 years as a professional player."
Not everyone thinks Zuniga's intentions were pure, though.
Brazilian legend Ronaldo said earlier Saturday it was a "violent" and "unlawful" challenge.
Neymar dreams of holding trophy
Neymar also spoke for the first time since the incident, thanking everyone for their messages of support.
"I'm certain that my teammates will do everything possible so that my dream, which is to be a champion, comes true.
"My dream was also to play in a World Cup final but this time it didn't work out," the 22-year-old said, his voice cracking with emotion.
"But God willing, they're going to win this, they're going to be champions, and I'm going to be by their side, with them. And all us Brazilians are going to be celebrating."