Culleton is accused of making a fraudulent claim on nomination forms when he ran in this year’s election.
The Constitution prohibits any person who is insolvent or an undischarged bankrupt from serving in parliament.
A warrant has been issued for Culleton’s arrest. He was due to appear in court in Perth last week but did not show up.
AFP Detective Acting Superintendent Andrea Coleman said Culleton is alleged to have falsely declared his financial circumstances on nomination forms, specifically that he was not an undischarged bankrupt.
“The AFP will allege the man made a fraudulent claim on nomination forms as part of an attempt to be elected as a senator in the recent Federal Election,” Coleman said.
“The AFP is dedicated to protecting democracy and officers will lay charges if they have evidence that someone committed an offence to mislead the community or gain a benefit.”
If found guilty, he could face a maximum of a year in jail.
Culleton was elected as a One Nation senator in the 2016 federal election, but resigned from the party to serve as an independent soon after.
He was forced out of the Senate after it was revealed he was bankrupt.
He then formed the Great Australian Party, which received 0.55 per cent of the national vote on the Senate ballot in this year’s election.