The Napoli full-back fractured one of the Selecao star's vertebra during his side's 2-1 loss to the tournament hosts during their quarter-final on July 4 in Fortaleza.
Zuniga avoided further punishment, but his knee into Neymar's back has been heavily criticised 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) has now defended the 28-year-old.
"FCF rejects all threats and insults against the player Juan 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 faced no sanction from Fifa as the referee had 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 on Tuesday.