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.
Dubai’s Roads and Transport Authority (RTA) has announced plans to install battery-swapping stations for electric bikes across key locations in the emirate.
The UAE and Azerbaijan have taken a major step forward in their bilateral relations, announcing a Comprehensive Strategic Partnership during a high-level meeting in Karabakh.
His Highness Sheikh Hamdan bin Mohammed bin Rashid Al Maktoum, Crown Prince of Dubai and the UAE's Deputy Prime Minister and Defence Minister, has directed Dubai Civil Defence to meet the highest global standards in community protection.
At the Emergency Arab-Islamic Summit, the UAE reaffirmed its full support for Qatar in the wake of the recent Israeli strike on Doha, calling the attack a blatant violation of international law and regional sovereignty.
His Highness Sheikh Dr. Sultan bin Mohammed Al Qasimi, Supreme Council Member and Ruler of Sharjah has announced 'Majma' Al-Tawarikh' (The Arabic Encyclopedia), a new historical project that will serve the Arab world by chronicling events from 550 BCE onwards.
His Highness Sheikh Mansour bin Zayed Al Nahyan, Vice President, Deputy Prime Minister and Chairman of the Presidential Court, is leading the UAE delegation at high-level meetings in Doha.