Hubert's vehicle was in collision with the cars of the Juan Manuel Correa and Marino Sato in the second lap of the race.
"The scene was immediately attended by emergency and medical crews, and all drivers were taken to the medical centre," said the FIA statement.
"As a result of the incident, the FIA regrets to inform that the driver of car number 19, Antoine Hubert, succumbed to his injuries."
Correa, who suffered leg fractures in the crash, was taken to the CHU hospital in Liege. The 20-year-old American was reported to be in a stable condition. Sato, also 20, was unharmed.
Hubert signed for the British stable BWT Arden in January 2019 for the Formula 2 campaign.
He started the first race of the season at Sakhir in eleventh position but finished fourth. He went on to win races back-to-back races in Monaco in May and a month later at Le Castellet in his native France.
"I can't believe it," tweeted the French driver Esteban Ocon. "We're the same age. We started at the same time and have driven against each other for years. All my thoughts are with his family. RIP Anthoine."