Yann Arnaud, 38, was taking part in a performance involving aerial straps on Saturday when he fell.
The French performer died in hospital later. "The entire Cirque du Soleil family is in shock and devastated," a statement said.
The company said it was working with local authorities to investigate what had gone wrong.
It has cancelled two shows scheduled for Tampa on Sunday.
Arnaud had been with the Cirque du Soleil for over 15 years.
He "was loved by all who had the chance to know him", company CEO, Daniel Lamarre said.
This is not the first time a member of the Cirque du Soleil has died in an on-stage incident.
In 2013, a performer died after falling off a stage in Las Vegas.
And the son of a Cirque du Soleil founder died in December 2016 after being accidentally crushed by a telescopic lift.
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