|Lt Moaz al-Kasasbeh had been held hostage since his plane came down on 24 Dec.|
The video, which could not immediately be verified, shows a man standing in a cage and engulfed in flames.
Lt Moaz al-Kasasbeh was captured when his plane came down near Raqqa, Syria, in December on a mission to support the US-led military coalition against IS.
Jordanian state TV confirmed the death and said he was killed a month ago.
The video posted online on Tuesday was distributed via a Twitter account known as a source for IS propaganda.
A relative of Lt Kasasbeh told Reuters news agency that the Jordanian armed forces had informed the family that he had been killed.
The BBC's Frank Gardner says that the video is clearly intended to shock.
The highly produced 22-minute film includes a sequence showing the Jordanian pilot walking at gunpoint amongst rubble apparently caused by coalition air strikes that targeted jihadists.
Jordan had been attempting to secure Lt Kasasbeh's release as part of a prisoner swap.
It had offered to free Sajida al-Rishawi, who is on death row in Jordan for her role in hotel bombings in Amman in 2005, in return for the release of Lt Kasasbeh.
The video emerged three days after another video appeared to show the dead body of Japanese hostage Kenji Goto.
The US state department said it was working to confirm the authenticity of the video.
US President Barack Obama said in a statement that if the video was real, it would be "one more indication of the viciousness and barbarity" of IS.
"I think it will redouble the vigilance and determination of the part of the global coalition to make sure they are degraded and ultimately defeated," he added.
Kevin Connolly, BBC Middle East Correspondent
|Safi Yousef, father of Jordanian pilot Moaz al-Kasasbeh, in Amman, 30 Jan. 2015|
Relatives had gathered around Lt Kasasbeh's father
After the murder of Japanese journalist Kenji Goto the mood darkened, and one of the pilot's uncles, retired police general Fahd al-Kasasbeh, was close to tears as he asked the BBC to help relay a direct appeal to the hostage takers.
There were family members who hoped Lt Kasasbeh would be treated with lenience because he was a Muslim, while others feared he'd be harshly dealt with as an enemy pilot. And all along on both sides of the argument was the nagging fear that no proof of life was received, no photographs and no video.
The family's reaction, of course, will be one of deep grief and distress. But in wider Jordanian society, there will be pressure for the government to hit back. An implicit threat to speed up the execution of IS prisoners in Jordanian jails, where some are already on death row, may now be carried out.