A Syrian army statement released on Syrian state television said the plane crashed and the pilot was missing in the first such downing of a Syrian jet by the United States since the start of the conflict in 2011.
The army statement said it took place on Sunday afternoon near a village called Rasafah.
The "flagrant attack was an attempt to undermine the efforts of the army as the only effective force capable with its allies ... in fighting terrorism across its territory," the Syrian army said.
"This comes at a time when the Syrian army and its allies were making clear advances in fighting the Daesh terrorist group," it added.
The U.S. Central Command later issued a statement saying the Syrian plane was downed "in collective self-defense of Coalition-partnered forces," identified as fighters of the Syrian Democratic Forces (SDF) near Tabqah.
It said that "pro-Syrian regime forces" had earlier attacked an SDF-held town south of Tabqa and wounded a number of fighters, driving them from the town.
Coalition aircraft in a show of force stopped the initial advance. When a Syrian army SU-22 jet later dropped bombs near the U.S.-backed forces, it was immediately shot down by a U.S. F/A-18E Super Hornet, the statement said.
Before it downed the plane, the coalition had "contacted its Russian counterparts by telephone via an established "de-confliction line" to de-escalate the situation and stop the firing."
The coalition does "not seek to fight the Syrian regime, Russian or pro-regime forces" but would not "hesitate to defend itself or its "partnered forces from any threat," the statement said.