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"Given the severity of the accident, there are no survivors. We have recovered four bodies so far," Police Major Jorge Andrade said, according to AFP.
The crash happened around 13:00 local time (19:00 BST) in the Pueblo Viejo region after the plane departed from an airport in Pisco, Peru.
Video from Reuters news agency shows firefighters spraying water at the scene as smoke rises from the wreckage.
In a statement in Spanish posted online by the Municipalidad Provincial de Nasca, officials expressed "deep sorrow" for the accident and extended "heartfelt condolences to the families of the deceased".
The statement said the plane belonged to local Peruvian airline Aerodiana.
In a statement, the airline said it would "assess its flight schedule in accordance with the directives of the relevant authorities", according to Reuters.
The BBC has contacted the airline for comment.
This isn't the first plane to crash over the famed site in the past few decades.
In 2022, another small tourist plane crashed during a flight over the Nazca Lines site, killing seven on board.
And in 2010, a tourist plane went down over the site, killing six people on board.