The Group C rivals will meet in the United States in order to step up their preparations for the competition in Chile, which kicks off on June 11.
Two-time South American champions Peru meet Brazil in their opening match in Group C, which also in includes Colombia, but are still to appoint a head coach following the departure of Pablo Bengoechea at the end of 2014.
"We just closed the deal with the Federation of Venezuela to play on March 31 in Miami," national team sports manager Antonio Garcia Pye told reporters.
He added: "It is vital that we find a head coach, as there will be a very short time to prepare for the upcoming tournament."
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