"We have confirmed reports that IS members took a (non-Syrian) Arab pilot prisoner after shooting his plane down with an anti-aircraft missile near Raqa city," the Syrian Observatory for Human Rights said.
The IS branch in Raqa published photographs on jihadist websites purporting to show its fighters holding the captured pilot, with a caption identifying him as Jordanian and giving his name.
Several photographs were released, including one showing the pilot, wearing only a white shirt, being carried from a body of water by four men.
The jihadists claimed to have shot down the warplane with a heat-seeking missile.
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The Britain-based Observatory, which relies on a wide network of sources inside Syria, had no further immediate information.
There was no immediate reaction from authorities in Jordan.
Jordan is among a number of countries that have joined the US-led alliance carrying out air strikes against IS after the jihadists seized control of large parts of Syria and Iraq.
Saudi Arabia, the United Arab Emirates, Jordan and Bahrain are taking part in the air strikes in Syria alongside the United States.
The Sunni extremist IS has committed widespread atrocities in areas under its control, including mass executions of captured soldiers and public beheadings of hostages including Western journalists and aid workers.
Coalition warplanes have carried out regular strikes around Raqa, which IS has used as the headquarters for its self-proclaimed "caliphate".