CAS said on Friday it had partially upheld an appeal filed by the Werder Bremen player who served a three-month ban for the incident, which according to the Peruvian Football Federation (PFF) followed a World Cup qualifier against Brazil in 2007.
"The CAS Panel noted that the facts put forward by the PFF in relation to Pizarro were not supported by concrete evidence," the top sports court said in a statement.
"Furthermore, the panel also noted that the incidents reported by the PFF were not dealt with either in the PFF regulations, or in the FIFA regulations. Accordingly, the CAS has cancelled the fine of $10,000."
The Chelsea striker, on loan at Werder Bremen, has denied any involvement in the incident, or even being aware of it.
He was initially handed an 18-month ban along with fellow strikers Jefferson Farfan and Andres Mendoza and defender Santiago Acasiete.
The bans on Pizarro, Farfan and Acasiete were later cut to three months and the fine reduced from $80,000 to $10,000.
