Hours after players read out anti-racist messages before the South American showdown, Zuniga was called 'black b******', 'monkey' and 'slave', with several messages including threats to kill the defender.
There had been fears for Zuniga's safety as Colombian officials flew the defender home after his team's 2-1 loss to Brazil on Friday during the quarterfinal, the Daily Star reported.
The offensive insults came after the full-back charged into Neymar and fractured the striker's vertebra.
Zuniga later apologised and said that he never meant to hurt Neymar.
However fans, fearing riots on the streets if Brazil goes out against Germany in the semi-final on Tuesday, were soon gunning for Zuniga.
A fan tweeted 'Zuniga you f***** black scrotum', adding that scumbags die early and that he would kill the defender.
The Tweet also called Zuniga a 'black mother f****r' and a 'f***in c**k-sucking whore'.
Other fans also tweeted death treats for the defender with some calling him a 'monkey from Colombia' that robbed Neymar's glory and also that this 'f****** ugly Blackman deserves to be shot'.
In one image on Twitter two girls posed with kitchen knives with the words 'where's Zuniga, let's kill Zuniga.'
The abuse continued with a fan posting that Zuniga can consider himself a dead man, adding that if no one kills him, witchcraft would.
Zuniga has locked the account now so that it can no longer be accessed, the report added.