A Derbyshire Police spokesman said the collapse happened at 1950 BST on Saturday.
He said: "Reports indicated strong winds lifted part of the roof off the stage.
"Three people were injured and were taken to the Derby Royal Infirmary."
Sally Booth, site manager, said a "freak gust of wind" hit the main stage.
She said: "It's been raining and windy all day but this was a freak gust of wind that was capable of knocking people over."
Helen Hat, a spokesperson for festival organisers Spring Productions, said on Sunday: "There was great concern last night... but now the mood is fairly buoyant.
"We are very happy that we're going ahead."
Huge squall
Gerard Baker, a chef at a cafe on the site, witnessed the stage roof collapse.
He 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."
Mr Baker said he was about 15m from the main stage when it was "pretty much wrecked".
"The supports from the marquee were ripped out from the ground and the wires broke," he said.
He said it was thought the people hurt were crew who were on stage setting up for the next band.
Several others who saw the roof fall posted comments online after the incident.
Pak Chan wrote: "Have survived the great gust of wind that's wiped out the Bearded Theory festival. Am huddled in tent, awaiting weather Armageddon."
The festival, now in its second year, features a range of music including dance, rock, folk and acoustic.
Organisers said this year's event had attracted a capacity crowd of 2,500.
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