Zuniga fractured Brazil star Neymar's vertebra during Colombia's 2-1 loss to the FIFA World Cup hosts in a rough quarter-final on July 4.
The Napoli defender avoided further punishment, but his knee into Neymar's back has been slammed and was labelled a "coward's tackle" by Brazil captain Thiago Silva.
Zuniga said it was a "normal" challenge and the Federacion Colombiana de Futbol (FCF) defended the 28-year-old.
"FCF rejects all threats and insults against the player Camilo Zuniga and his family," the national body said in a statement on Wednesday.
"It [FCF] will continue taking all actions with the appropriate security and government organisations to give the necessary guarantees to the player, for both his time in Colombia and his permanent residency in Italy."
Napoli have also come out in support of Zuniga, who went unpunished by FIFA due to the referee having already ruled on the incident.
Brazil will face the Netherlands in the third-place play-off after the hosts were thrashed 7-1 by Germany in the semi-finals.
