Reuters could not immediately confirm the content of the video, which showed a man resembling airman Mouath al-Kasaesbeh standing in a black cage before being set ablaze. But the reaction of the Jordanian authorities made clear they treated it as genuine.
"The revenge will be as big as the calamity that has hit Jordan," army spokesman Colonel Mamdouh al Ameri said in a televised statement confirming the death of the pilot, who was captured in December when his plane crashed over Syria.
A government spokesman said in a statement that Jordan would deliver a "strong, earth-shaking and decisive" response.
The fate of Kasaesbeh, a member of a large tribe that forms the backbone of support for the Hashemite monarchy, has gripped Jordan for weeks and provoked rare protests against King Abdullah over the government's handling of the crisis.
The king cut short a visit to the United States to return home.
The head of the Jordanian armed forces broke the news of the pilot's death to his family, a relative told Reuters.
Jordan had said last week it was killing to hand over an Iraqi woman detained for a role in a 2005 suicide bombing in Amman, if Islamic State would release the pilot.
But Jordanian state TV said on Tuesday that he had been killed a month ago, on Jan. 3.
The White House said the intelligence community was studying when the video was recorded and that President Barack Obama had ordered his team to devote all resources to locate other hostages held by Islamic State.
A staunch U.S. ally, Jordan is part of the alliance against the Islamic State group that has seized large areas of Syria and Iraq. King Abdullah has defended the campaign from domestic criticism, saying that moderate Muslims need to combat a group whose ideology and brutality have insulted Islam.
Obama said the video, if real, would redouble the determination of a U.S.-led alliance to degrade and destroy Islamic State. He said it would be another sign of the "viciousness and barbarity" of the militants.
"Whatever ideology they're operating off of, it's bankrupt," Obama told reporters.
STRING OF VICTIMS
In the video, the burned man wore orange clothes similar to those worn by other foreign Islamic State captives who have been killed since the U.S.-led coalition started bombing the militants in July.
Islamic State has released videos showing the beheadings of five U.S. and British hostages and said that it has killed two Japanese captives in the same way. It has meted out the same treatment to many more Arab prisoners, including Syrian government soldiers.
The militants have stepped up the gruesome killings while coming under increased military pressure from U.S.-led air strikes and a push by Kurdish and Iraqi troops to reverse their territorial gains in Iraq and Syria.
Jordan had been demanding the release of Kasaesbeh in exchange for Sajida al-Rishawi, jailed in Jordan for her role in a 2005 suicide bomb attack that killed 60 people.
Islamic State had previously demanded Rishawi's release in return for the life of Japanese hostage Kenji Goto. The beheading of Goto, a veteran war reporter, was shown in a video released by the group on Saturday.
In the Islamic State video, Kasaesbeh is interviewed, describing the mission he was due to carry out before his jet crashed. The video also showed footage of the aftermath of air strikes, with people trying to remove civilians from debris.
A man resembling Kasaesbeh is shown inside the cage with his clothes dampened, apparently with flammable liquid, and one of the masked fighters holds a torch, setting alight a line of fuel which leads into the cage.
The man is set ablaze and kneels to the ground.
Fighters then pour debris, including broken masonry, over the cage which a bulldozer then flattens, with the body still inside. The video showed a desert setting similar to previous videos of killings.
Islamic State grew out of the Sunni-Shia conflict in Iraq and the civil war in Syria, in which an estimated 200,000 people have been killed since 2011.
The Syrian Observatory for Human Rights monitoring group said on Tuesday that 51 civilians, including children, had been killed by Syrian air force strikes inside the country within the past day.
The U.S.-led coalition says it does not coordinate with the Syrian government and has called for the removal of President Bashar al-Assad. It does work with the Iraq government, which is also fighting Islamic State.