The Frenchman, who was 22, suffered a huge impact from the car of American Juan Manuel Correa at about 170mph at the Raidillon swerves.
An FIA statement said that Hubert was taken to the medical centre after the incident, and died at 18:35 local time.
Correa was taken to Liege hospital and is in a stable condition, the FIA said.
The race was stopped after the crash and cancelled within a few minutes when the potential seriousness of the accident became clear.
Hubert, who drove for the BWT Arden team, was lying eighth in the championship and had scored two wins this season, in Monaco and France.
Racing drivers and motorsport teams have paid tribute on social media.
Former F1 driver Fernando Alonso posted on Twitter: "What a sad afternoon. I have no words. It hurts the heart. Rest in peace, champ."
Lewis Hamilton wrote on Instagram: "This is devastating. God rest your soul Anthoine. My prayers and thoughts are with you and your family today.
"If a single one of you watching and enjoying this sport think for a second what we do is safe your hugely mistaken. All these drivers put their life on the line when they hit the track and people need to appreciate that in a serious way because it is not appreciated enough.
"Not from the fans nor some of the people actually working in the sport. Anthoine is a hero as far as I'm concerned, for taking the risk he did to chase his dreams. I'm so sad that this has happened. Let's left him up and remember him. Rest in peace brother."
BBC Sport
More about: F2
