In a statement, Burning Man said Mitchell was pulled from the flames by firefighters and airlifted to University of California-Davis' burn treatment center.
Festivalgoers looked on in horror as the man raced towards a burning giant wooden effigy and was engulfed by the fire.
Meanwhile, the main road to Burning Man remains open Sunday morning as the annual counter-culture festival winds down and an estimated 70,000 participants start to head home.
Burning Man is a week-long festival in a temporary city erected in the desert about 100 miles north of Reno.
Allen said doctors confirmed Mitchell wasn't under the influence of alcohol, but a toxicology report was pending.
The Burning Man organization canceled scheduled burns through noon Sunday but will proceed with the scheduled Temple burn at 8 p.m. Sunday night.
The festival culminates with the burning of a towering 40-foot effigy made of wood, a symbol of rebirth, which usually happens the Saturday before the Labor Day holiday. Despite the self-parodying aspects of the festival, the metaphor of Burning Man has rarely achieved such existential heights. This year's festival ends on Monday.