Wyatt Roy was condemned by Prime Minister Malcolm Turnbull and Foreign Minister Julie Biship after SBS News revealed he was caught in a gun-fight between Kurdish Peshmerga forces and fighters from the so-called Islamic State near Sinjar, close to the Syrian border.
The Kurdish-controlled area he visited is near Mosul, which is a declared conflict zone under Australian law, meaning Australian citizens are legally banned from entering.
During Senate estimates, Greens Senator Nick McKim asked Australian Federal Police Commissioner Andrew Colvin whether Mr Roy was being investigated.
"We're very conscious that it was a high profile matter and we did our own due diligence to satisfy ourselves, but no we don't have a current open investigation in relation to that," Commissioner Colvin told the hearing.
"Based on the public reporting we did form a conclusion that we didn't believe any offences had been committed.
"I guess I should leave commentary about the appropriateness of the activity to the government, which they have made comment on but we have no active investigation in relation into his movements."
Mr Turnbull blasted Mr Roy for the trip last month.
"I'm disappointed in Wyatt, he shouldn't have gone to Iraq," he said.
"He was acting in defiance of government advice. It was very stupid.
"Australians should not go to those parts of the world."
He Turnbull said he would be giving some "very sage and stern advice" upon Mr Roy's return to Australia.
Foreign Minister Julie Bishop said former Liberal frontbencher Wyatt Roy's trip to Iraq was "irresponsible".
"He has placed himself at risk of physical harm and capture, and acted in defiance of government advice," Ms Bishop said.
At Monday's hearing, Attorney-General George Brandis said Senator McKim's question was not appropriate.
"Mr Roy is a private citizen and was a private citizen at all relevant times," Senator Brandis said.
"I just wonder why the affairs of a private citizen, who is not under investigation... should be a matter for this estimates committee."
Mr Roy has since staunchly defended his trip to the Kurdish-controlled region, saying he wanted to educate himself about the conflict and support the Kurds with resources and in their fight for statehood.
