The fatalities included 36 people who died on site, and another person who succumbed in hospital, said Walther Oporto, Arequipa's regional health chief, citing firefighters at the scene of the accident, Reuters reported.
The death toll was among the highest in a series of bus accidents in recent years in Latin America, and one of the worst recorded in Peru.
Among the injured were an eight-month-old baby and two other children, according to a list shared by local authorities.
The bus company, Llamosas, did not immediately respond to a request for comment.
Authorities said the bus was traveling on the highway from the coastal town of Chala to the region of Arequipa when it struck a van. The impact sent it careening into a ravine around 200 meters (656 feet) deep.
Photos published by the local government showed the bus overturned at the bottom of the gully amid scattered car parts and passenger belongings.
The Arequipa government said 26 people were being treated for injuries, three of them in serious condition.