The former detainee has been referred to Australian Federal Police.
More than 140 people have been released into the community after the High Court ruled indefinite detention was illegal.
The landmark decision triggered emergency laws that were rushed through parliament, subjecting the people released to surveillance and strict curfews.
Five people have refused to wear the ankle monitors.
Efforts were being made to track down the missing detainee, Immigration Minister Andrew Giles said. (Lukas Coch/AAP PHOTOS)
The immigration minister was quizzed about the missing person during Question Time.
Opposition frontbencher Dan Tehan asked when the government was first made aware.
"Does the minister know where this individual is now?" he said.
Andrew Giles refused to bite, saying the government would not comment on individuals or operational matters.
"The Australian community should be assured that all efforts ... are being made to track down this individual," the minister said.
The High Court on Tuesday released its reasons for the indefinite detention ruling, which overturned 20 years of legal precedent.
The court found the government contravened the Constitution on the basis that detention was punitive "in circumstances where there was no real prospect of the removal of the plaintiff from Australia becoming practicable in the reasonably foreseeable future".
The government is expected to pursue alternative laws to lock up serious criminals released from immigration detention, fearing a risk to community safety.
As well, the government has set aside $255 million to enforce strict visa conditions on the released detainees, some of whom are convicted murderers and sex offenders.
Asylum seekers and refugee advocates are demanding the government hold a royal commission into immigration detention.
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