The sides are due to meet twice in the space of four days, with the second fixture scheduled for Monday, but Bayern Munich striker Pizarro will be absent for both.
It was confirmed last week that the 75-cap forward would be sidelined for "several weeks" after suffering a tear in his right thigh.
The news will have come as a blow to national team coach Pablo Bengoechea, who is looking to build on a promising run of form of late.
Peru have won four of their last five fixtures, with the only defeat coming away at World Cup surprise package Chile last month.
The 54th-ranked nation followed up that defeat with a 1-0 win over Guatemala, and Bengoechea says his hunger for victory is unwavering, despite the friendly status of the Paraguay fixtures.
"Our intention, every time we play a friendly match, is to improve," he said. "Nobody wants to lose in football.
"It is easier to improve with a victory than with a loss."
In contrast to the in-form Peru, Paraguay have endured a torrid run of results since their unsuccessful World Cup qualifying campaign.
Victor Genes' side have won just one of six friendlies since that qualifying process came to an end, and have just two victories from their last 14 international fixtures.
Having occupied a higher position in the FIFA world rankings since 1995, Paraguay have seen Peru overtake them and extend their lead over the last two years.
Peru now sit 22 places higher than Paraguay. Plenty to prove, then, for Genes' men in the forthcoming friendly fixtures.
The teams met twice during World Cup qualifying, with Paolo Guerrero scoring twice in a 2-0 home win for Peru in October 2011, before Pablo Aguilar scored the only goal as Paraguay claimed the reverse fixture.
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