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.
The United Arab Emirates has strongly condemned a car-ramming attack that occurred during a Filipino community festival in Vancouver, Canada, resulting in fatalities and injuries.
Teams from Abu Dhabi Police and the Abu Dhabi Civil Defence Authority successfully brought under control a fire that broke out on Sunday afternoon at Al Wahda Mall in Abu Dhabi.
The 32nd edition of Arabian Travel Market (ATM) will open on Monday 28th April at Dubai World Trade Centre, welcoming more than 2,800 exhibitors and over 55,000 travel professionals from 166 countries.
President His Highness Sheikh Mohamed bin Zayed Al Nahyan has sent a message of congratulations to Cyril Ramaphosa, President of the Republic of South Africa, on the occasion of his country's Independence Day.
Dubai’s Roads and Transport Authority, in partnership with Etihad Rail, has opened a 1.8 km-long flyover to improve traffic flow on Al Yalayis Street and around Dubai Investments Park (DIP).
Dubai’s Roads and Transport Authority (RTA) will be carrying out a planned emergency drill at the Gold Souq Metro Station on Sunday, April 27, between 1:00 AM and 5:00 AM.