Venezuelan President Nicolas Maduro accused Peru's authorities of "xenophobia" against the national team and its fans.
"The xenophobia of that racist oligarchy of Peru has been unleashed against our noble team. Venezuela has raised its voice to protest against xenophobia, violence and aggression," Maduro said.
Venezuela's relations with Peru have been strained, especially since the ouster of leftist President Pedro Castillo in 2022 and the inauguration of successor Dina Boluarte.
Tuesday's game marked a tumultuous night for the South American qualifiers, following a match between Brazil and Argentina in Rio de Janeiro which saw ugly clashes between fans.
Venezuelan footballer Nahuel Ferraresi earlier showed bandages on his right hand, saying Peruvian police "beat me."
"These are things which should not happen. The match was over and we went to thank our Venezuelan supporters," he said.
Ferraresi said another player had handed his jersey over to fans, and he was about to throw his to the crowd when the police blocked him.
"Then others got angry, I don't know what happened, and (the police) took out their batons to hit us. They hit me twice... but it's not a serious injury."
Videos of the incident, which show Peruvian police officers brandishing their batons against the players, have gone viral on social media.
Venezuela's football federation condemned "acts of discrimination and xenophobia" against the team and their fans, including the injuring of Ferraresi by a police officer.
The country's sports ministry said it was "embarrassing that a football event of such importance has been used as a battlefield to expose the basest passions of anti-Venezuelan xenophobia."
Sports minister Mervin Maldonado said the football federation had communicated to world football governing body FIFA about the match's aftermath.
Upon his return to Venezuela, Navarro called the police incident with his teammates in Lima a "total disgrace."
Tensions had worsened on Wednesday when the Venezuelan team's Rutaca airline plane was delayed for almost four hours.
The delay "occurred for purely administrative reasons related to fuel supply," the company that operates Jorge Chavez International Airport in Lima said, denying it was a result of "security controls."
Venezuela's Foreign Minister Yvan Gil described the delayed flight as a "kidnapping."
After the draw, Peru is in last place in the qualifiers, while Venezuela -- which has never qualified for a World Cup -- is in an unprecedented fourth place.
Before the match, Peruvian police carried out an unusual identity check among fans, and were accused of targeting Venezuelans.
The move came a week after a controversial decree came into force authorizing the government to expel foreigners.
Peru is home to some 1.5 million Venezuelan immigrants, many of whom have fled an economic crisis at home.
© Agence France-Presse
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