Mu'ath Al Kassasbeh was taken captive by IS when his F-16 fighter jet crashed near Raqqa, Syria, in December.
Images of his murder have been circulated by IS supporters on Twitter.
The fuel is then lit and the cage bursts into flames.
The Jordanian government has informed his family he has been killed and vowed an "earth-shattering" response against IS.
"The blood of the martyr will not have been shed in vain and ... vengeance will be proportional to this catastrophe that has struck all Jordanians," said army spokesman General Mamduh al Amiri.
Jordanian state TV said Mr Al Kassasbeh was murdered on 3 January. Other reports said it was 8 January.