The attack, which targeted a market near a mosque in Baghdad, killed three and injured dozens.
The Islamic State of Iraq and Syria claimed responsibility for the bombing and, in a tweet, identified the bomber by his nom de guerre: Abu Bakr al-Australi.
An Australian teen's involvement in the bombing was a "disturbing development," Australia's Attorney General, George Brandis, said in a statement.
Brandis condemned the attacks undertaken by ISIS, (also called ISIL), and said the government "is deeply concerned about the involvement of Australians in these activities."
The attorney general also voiced concern that Australian foreign fighters can pose "a significant domestic security threat to Australia when those involved return home and seek to pursue violence here."