Another bus and a refrigerator truck slammed into the buses soon after, said emergency coordinator Oscar Gonzalez.
"Preliminary investigations indicate the driver that crossed into the opposite lane likely fell asleep," Gonzalez said.
The crash took place early Monday on kilometer 315 of the Panamerican Norte highway near the coastal town of Huarmey, authorities said.
A group of Senegalese and evangelicals with the Worldwide Missionary Movement were involved in the crash, local media reported.
Deadly bus accidents are common in Peru, where transportation regulations are weak.