South Western Ambulance Service said it did not know how the incident involving the man - thought to be in his 20s - happened.
Great Western Air Ambulance flew him to Queen Elizabeth hospital in Birmingham after the ambulance service was called at about 17:10 BST.
Wiltshire Air Ambulance had also been called after the man suffered significant burns at the Somerset site.
Final preparations are taking place for the 2016 edition of the festival which opens its doors to the public on Wednesday.

Brookfield Renewable UK applied to develop a site at Larbrax, near Leswalt in Wigtownshire.
Dumfries and Galloway Council's landscape architect objected to the plans, claiming it would have an adverse visual impact on the surrounding coastal area.
Scottish Natural Heritage also raised "significant and serious concerns".
A spokesman for Brookfield Renewable UK said: "It is disappointing that the Dumfries and Galloway planning committee have failed to recognise both the many positive long-term economic benefits the Larbrax Wind Farm would bring to the Wigtownshire area, and also the limited effects of the proposal.
"We appreciate that there is frustration locally following the decision and we would like to thank local residents and businesses for the time and support that they have afforded the project over the last three years.
"We maintain our position that this is an acceptable and beneficial scheme and we will now carefully consider our next steps."
Meanwhile, a separate proposal for a wind farm at Gass Farm, north-east of Glenluce, has been approved.
Councillors backed WilloWind's plans for the nine-turbine development, subject to strict conditions.
A man has suffered severe burns at the Glastonbury Festival site.
[NEXT_CONCEPT]
Plans to build eight new wind turbines in the far south-west of Scotland have been rejected by councillors.