The footage shows people dancing in the club before sparks from onstage fireworks ignite the building's ceiling.
Svetlana Kuvshinova, who was in the club when the fire began, said the flames "took seconds to spread".
"It was like a dry haystack. There was only one way out. They nearly stampeded me," the Associated Press quoted her as saying.
Another eyewitness told local TV: "When the merry-making started, when they were warming up, they set off fireworks.
"When I turned back, I saw drops falling off the ceiling and then there was a lot of smoke. Later this huge flame was moving along the ceiling," the unnamed woman said.
Regional public security minister Igor Orlov told Itar-Tass news agency: "People panicked and succumbed to burns, general crush and gas poisoning."
A spokesman for the prosecutor-general's main investigative unit told the news agency that it was not a terrorist attack.
The Russian government has set up a special commission to deal with the incident.
Regional officials said that fireworks used at the party were too powerful for enclosed premises and were intended for outdoor use.
Perm has a population of 1.2 million and is the sixth largest city in Russia.
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