Highway police commander William Vasquez said the bus was traveling to the northern city of Querocoto.
A witness to the crash, Emiliano Fernandez, told radio station Canal N that he saw the bus swerve off the road.
"When we got to the canyon to help, we only heard the cries of the people from the bottom," he said.
Rescuers transported 23 survivors with injuries to nearby towns including Chiclayo for treatment.
Local media say it may be difficult to account for all the passengers because the bus company did not keep complete records.
Deadly bus wrecks are common in Peru because of rundown vehicles, poorly maintained roads and reckless driving.
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