A Derbyshire Police spokesman said the injuries suffered included a suspected broken wrist, shoulder, back and neck injuries. A number of other people were treated for shock.
Police said the collapse happened at 1950 BST on Saturday 16 May. The stage was closed and made safe following the accident. Two other stages remained open and the festival continued.
Staff from the website efestivals.co.uk reported a freak gust of wind "described by one person as a twister" during a storm. Another witness quoted by the BBC said: "The sky darkened and within five minutes a huge squall came through, then it got seriously bad. The Portaloos started literally spinning through the air. It came with an astonishing suddenness."
On the rain-soaked opening day of the festival, prior to the stage collapse, a BBC reporter had spoken to first-night headliners Hawkwind, and asked about the bad weather. "This is nothing" said founder member Dave Brock, quoted on the BBC Online News website. "Once, at a gig in Germany, our drummer got blown off stage by the wind!"
Bearded Theory - which has a beard fancy dress theme - is a 2500-capacity charity event, now in just its second year. Organisers hoped to raise £5000 for homeless charity Shelter and Derby-based charity, the Padley Group.
A statement on the festival's website yesterday confirmed that all those taken to hospital the previous evening were back on site.
(Lee Baldock)