Judge Gerardo Mastrandrea said in the ruling seen by Reuters that the proceedings failed to reach "the minimum level of reasonable certainty as to the discriminatory content of the offence", and Acerbi was not sanctioned in any way.
Napoli said they were "astonished" by the decision.
"Napoli will no longer take part in merely decorative initiatives by soccer institutions against racism and discrimination; we will continue to address them alone, as we have always done, with renewed conviction and determination," the club said in a statement.
The Inter Milan player left the national team training camp on March 18th following the alleged incident and was replaced by AS Roma's Gianluca Mancini.
The incident reportedly occurred during a 1-1 draw between Serie A leaders Inter Milan and seventh-placed Napoli, with defender Jesus later saying that Acerbi had apologised, while Acerbi denied having used any racist language.
