Colombia's tournament ended on Tuesday in a penalty shootout loss to Switzerland in the round of 16.
During extra time, Campaz, who plays for Argentine club Rosario Central, missed a critical scoring opportunity when his shot went wide.
After the match, the player's social media accounts were flooded with negative comments and threats. He decided to limit comments on his social media and, as a precaution, did not take the return flight to his home country with his teammates.
"No athlete, nor any member of their inner circle, should be subjected to intimidation for representing their country in a sporting arena," the federation said in a statement.
On Instagram, Campaz shared a photo of himself covering his face in frustration, alongside a plea for respect.
"Football is also made up of difficult moments," he wrote. "My Colombia, please let us never lose sight of respect. We may think differently or feel frustration and sadness, but no passion justifies hatred or living in fear."
In response to the harassment, the Colombian federation has urged the country's attorney general's office to expedite an investigation to identify those behind the threats.
"Football must be a space for unity, respect, and hope - never a setting for hatred, intimidation or violence," the federation said, calling on fans to ensure that sporting disappointments never translate into real-world aggression.
The threats evoke a dark chapter in Colombian soccer history. During the 1994 World Cup in the United States, defender Andrés Escobar scored an own-goal in a 2-1 loss to the host nation.
Days after the team was eliminated and returned home, Escobar was murdered in Medellín.
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