The attack has raised fresh questions over the stability of pro-Western kingdom. According to the military, the blast happened t at about 5:30 am, near a makeshift tent encampment where tens of thousands of Syrian refugees are stranded.
The camp is known as Ruqban and has come up along an earthen barrier, or berm, which runs along the border in a remote desert area.
A booby-trapped car exploded at the berm, "killing and wounding a number of border guards," the military said in a statement.
It said several other "hostile" vehicles were destroyed, but did not give further details. No militant group has claimed claimed responsibility for the attack so far.
Terror outfit Islamic State controls large areas in neighbouring Syria and Iraq, and Jordan has beefed up security at the border to prevent attacks and infiltration attempts.