Zuniga's raised-knee challenge during a rough quarter-final when Brazil beat Colombia 2-1 left Neymar with a broken vertebra and out of the hosts' semi-final against Germany.
The 28-year-old right-back, who plays his club football with Napoli, sent his best wishes for a speedy recovery to Neymar and said there was no ill intent in the clash.
But there was a vitriolic reaction in some quarters, especially from Brazil, where current and ex-players called the tackle "cowardly" and "evil."
Brazil fans have also taken to social media to berate him.
"The Colombian Football Federation rejects all threats and insults against the player Camilo Zuniga and his family," the national body said.
"It reiterates it will continue taking all actions with the appropriate security and government organs to give the necessary guarantees to the player, for both his time in Colombia and his permanent residency in Italy."
Zuniga is currently on holiday in Colombia after the team's wonderful World Cup run and is due to return to Italy in days.
Earlier this week, FIFA ruled that he would not be retrospectively punished for the clash, noting it could not reopen the case because the referee had dealt with it on the pitch.
Sympathisers say Zuniga's foul on Brazil's marquee player was clearly not intended because TV replays showed he had his eye on the ball, but critics say it was reckless to have gone in with a knee up regardless of that.
The referee gave a foul but no card.
Neymar was in fantastic form up to that moment, having scored four goals in the tournament and been easily Brazil's outstanding performer.
Most Brazilians, however, agreed it was suspended captain and defender Thiago Silva who was missed even more in Tuesday's shocking 7-1 semi-final mauling by Brazil.
Napoli have also expressed solidarity with Zuniga, saying he does not deserve the "ferocious criticism" he has received for an "unfortunate ... but not malicious" incident.
— ESPN FC (@ESPNFC) July 10, 2014
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