The accident involved famed high-wire walker Nik Wallenda and several members of his family.
Authorities say Mr Wallenda was not injured.
Sarasota Fire-Rescue spokesman Drew Winchester said the group fell 30 or more feet, and four of the injured suffered trauma.
The group was practising a high-wire pyramid act in a tent for Circus Sarasota, which was set to open on Friday.
Local media reports said Nik Wallenda was the anchor for the pyramid when the accident happened.
Officials said he managed to catch himself and was not among the injured.
Authorities are investigating and said Mr Wallenda may make a statement later.
Pedro Reis, founder and chief executive of the Sarasota Circus Arts Conservatory which puts on the show, said during a news conference that nothing was wrong with the rigging but that some performers lost their balance.
He said the circus will open as planned.
"The show must go on," he said.
The Wallendas are considered the pre-eminent family of tightrope walkers.
This is not the first tragedy to strike the family. Patriarch Karl Wallenda died in a fall during a stunt in 1978 in Puerto Rico. Two other family members also died decades ago while performing.
Nik Wallenda said he trains like an athlete and calculates his risks for every stunt.
"I respect deeply what I do and realise there's a lot of danger in it," he said during a 2013 interview in Sarasota, his Florida home town.
In 2013, Wallenda successfully crossed a tightrope stretched across the Little Colorado River Gorge near the Grand Canyon. That walk was televised by the Discovery Channel. There was no safety net and Wallenda did not use a tether.
In 2012, Wallenda was the first person to cross a tightrope over the brink of Niagara Falls. Other daredevils have crossed the water further downstream but no one had walked a wire over the river since 1896. He did use a safety tether for that walk.
The Wallendas trace their roots to 1780 in Austria-Hungary, when their ancestors travelled as a band of acrobats, aerialists, jugglers, animal trainers and a bit later, trapeze artists.
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