Race organisers confirmed the fatalities after a three-vehicle incident close to the Peru-Chile border on Wednesday evening.
The taxi driver and a passenger died after the support vehicle hit them head-on, while a second taxi rolled several times as it swerved to avoid the crash.
Emergency services deployed three ambulances and a fire engine, and seven people were injured and taken to hospital in Tacna, Peru.
A Dakar Rally statement added: "An Antonov aircraft of the Peruvian police has been put on special alert to transport the injured to Lima, in coordination with the rally’s medical service.
"The Peruvian authorities have begun an inquiry into the accident in order to determine the exact causes."