Youssef al-Kasasbeh said he found out the news after the head of the RJAF informed another of his sons.
Lt Kasasbeh has been a pilot in the RJAF for six years and had only visited their home last Sunday, he said.
He appealed to IS leaders: "May Allah plant mercy in your hearts and may you release my son."
The air forces of Jordan, the US, UAE, Saudi Arabia, and Bahrain have carried out hundreds of air strikes on IS in Syria in the past three months.
Many of the targets have been in and around Raqqa, which is the de facto capital of the "caliphate" whose creation IS proclaimed in June.
Syrian government warplanes also regularly bomb Raqqa and the surrounding province. On Tuesday, an air strike killed more than 20 people, according to the Syrian Observatory.
Australia, Belgium, Canada, Denmark, France, the Netherlands and UK have joined the US in conducting air strikes on IS in neighbouring Iraq.
The BBC's Jim Muir in Beirut says the latest news will raise concern among the coalition nations about the level of armament available to the militants and the defensive measures deployed by coalition jets.
It may further diminish the appetite of Arab nations to take part in such operation, our correspondent adds.