Paris-born Sarah Guyard-Guillot was performing in the Ka show at the MGM Grand.
The 31-year-old acrobat and mother of two was pronounced dead late on Saturday night in hospital after falling 50ft (15m) from the stage.
Her death is believed to be the first fatality during a live performance in the show's 30-year history.
Witness Dan Mosqueda told the Las Vegas Sun that Ms Guyard-Guillot was being hoisted up the side of the stage when it appeared that she slipped free of her safety wire and plummeted to an open pit below.
"Initially, a lot of people in the audience thought it was part of the [show]," he said.
"But you could hear screaming, then groaning, and we could hear a female artist crying from the stage."
The show was stopped and audience members told that refunds or vouchers to future shows would be offered. All performances of Ka have been cancelled until further notice.
Cirque du Soleil founder Guy Laliberte issued a statement on Sunday praising the performer, who has been with the original cast since 2006 and has worked as an acrobat for 20 years.
"I am heartbroken. I wish to extend my sincerest sympathies to the family. We are reminded with great humility and respect how extraordinary our artists are each and every night," he said.
The Ka show combines dance, acrobatics and performance art with pyrotechnics and complex aerial displays and is a resident show in Las Vegas.
Millions of people around the world go to see touring and resident Cirque du Soleil shows every year.
A performer in the famous Cirque du Soleil has died after falling off a stage during a show in Las Vegas.