The attack was carried out by "a fighter of Islamic State," Amaq said in a statement.
It gave no further details.
The suicide bomber on Tuesday drove a car at speed across the border from Syria and rammed it into a military post.
The explosives-laden vehicle blew up a few hundred meters (yards) from a camp for Syrian refugees in a remote area where the borders of Iraq, Syria and Jordan meet, a Jordanian army statement said at the time.
It was the first such assault targeting Jordan from Syria since Syria's descent into conflict in 2011 and followed an attack on June 6 on a security office near the Jordanian capital Amman in which five people, including three Jordanian intelligence officers, were killed.
The incidents have jolted the Arab kingdom, which has been relatively unscathed by the instability that has swept the Arab world since 2011, including the expansion of Islamic State in Syria and Iraq.