Paiva was issued with a red card following the incident and will not be able to take any part in Brazil's quarter-final against Colombia on Friday, FIFA spokeswoman Delia Fischer confirmed.
FIFA's disciplinary committee was also investigating the incident, meaning Paiva could face further sanctions.
The fracas happened at half-time in Saturday's match, which Brazil won on penalties.
Chile's media spokesman Maria Jose said his Brazilian counterpart "hit" Pinilla.
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"I was not the only one involved. Pinilla came looking for me and I just defended myself," he was quoted as saying.
"I just pushed him," he added.
"They started to insult us, there was some shoving but no assault," Paiva said.