The Pershing County Sheriff’s Office said in a statement they believe the death was a “singular crime” but gave no further details.
They said updates would follow “while still preserving the integrity of the complicated investigation of a crime in a city which will be gone by the middle of the week”.
The New York Times reported several nearby attendees had been interviewed as the investigation continued.
Festival organisers said they were co-operating with authorities and advised attendees not to interfere.
“The investigation is ongoing, and the Pershing County Sheriff’s Office will be the primary source of further information.”
The week-long festival is scheduled to run through to tomorrow.
Now in its 38th year, the event has already faced safety concerns after a desert storm caused major damage to the site.
The possible homicide marks a dark moment in Burning Man’s history as the first alleged murder since the festival began in 1986.