Other sources said that four Israeli soldiers were injured, one seriously, in the shooting.
But the Jordanian Petra news agency quoted an unnamed military source as saying that no shots had been fired from Jordan.
The alleged attack comes 18 days into Israel's Gaza offensive and after sporadic attacks from within Israel's Arab neighbours.
Shots were fired at an Israeli army vehicle from Syria along the border on Sunday.
No one was hurt, but it was the second such attack on the Israel-Syria border since the start of Israel's assault on the Gaza Strip.
On January 8 four Katyusha rockets were fired from southern Lebanon into the northern Israeli city of Nahariya.
Israel and Jordan signed a peace agreement in 1994 and the border is usually quiet.