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.