His Highness Sheikh Hamdan bin Mohammed bin Rashid Al Maktoum, Crown Prince of Dubai and Chairman of Dubai Executive Council, posted a picture with Reffet saying "We will miss you".
In a statement posted on social media, the company said the 36-year-old French stuntman Vincent Reffet died "during training in Dubai" on Tuesday.
It added that he was a "talented athlete, and a much-loved and respected member of our team...Our thoughts and prayers are with his family and all those who knew and worked with him."
Jetman Dubai also said the company is working closely with "all relevant authorities."
Reffet came from a family of skydivers and was part of the "Jetman" team which performed groundbreaking stunts above the emirate using jetpacks and carbon-fibre wings.
The Jetmen have pulled off a series of dramatic flights, soaring in tandem above the Burj Khalifa, and alongside an Emirates Airbus A380, the world's largest commercial airliner.
Fans are also sending messages describing the wingsuit jumper as a legend and a hero.


Sharjah contains fire at commercial facility in Al Sajaa Industrial Area
Abu Dhabi responds to fire at construction site in Al Mushrif
UAE secures return of 6000 nationals amidst regional developments
കുർദിസ്ഥാനിൽ കോൺസുലേറ്റിനു നേരെയുണ്ടായ ഡ്രോൺ ആക്രമണത്തിൽ ശക്തമായി അപലപിച്ച് യുഎഇ
9 ബാലിസ്റ്റിക് മിസൈലുകളും 33 ഡ്രോണുകളും പ്രതിരോധിച്ചതായി യുഎഇ
UAE orders arrest of 10 for publishing misleading online content
UAE strongly condemns second drone attack on consulate in Iraqi Kurdistan
UAE tackles 9 ballistic missiles and 33 drones on Saturday
