Video footage shows a US F-15E Strike Eagle spiralling downwards as flames engulf its engine six miles from the US Ali Al Salem base.
The fighter pilot appears to have ejected and landed safely. The status of the other crew member, the weapons system operator, is unknown.
It is not known whether the jet was shot down by an Iranian missile, hit by friendly US air defence rockets or suffered a technical malfunction.
Three US soldiers have been killed and five more injured since operations started on Saturday morning.
Donald Trump vowed to avenge their deaths but warned there would likely be more casualties before the war comes to an end.
The war expanded on Monday after Israel attacked Lebanon in response to Hezbollah firing retaliatory strikes over the killing of Iranian supreme leader Ali Khamenei.
