The Australian Federal Police (AFP) have not commented on the content of the conversation, which was streamed live on Periscope.
But the West Australian newspaper said it was clearly about the operation to arrest Chan Han Hoi last weekend.
The paper said it had alerted police.
Mr Choi, 59, was arrested in Sydney on Saturday. He has been charged with being an “economic agent” for North Korea, in the first case of its kind in Australia.
Police believe he had been in contact with “high ranking officials in North Korea”.
The Federal Police confirmed to the BBC only that “part of an office conversation was accidently broadcast via the AFP’s Periscope account” on 13 December.
A spokesperson said this happened when a piece of “social media broadcasting equipment” was being tested.
The West Australian said the AFP’s Twitter account sent out a link when the broadcast began on Periscope.
The tweet was quickly deleted, but a minute-long Periscope recording remained online until the paper alerted police. It said about 40 people had heard the broadcast.
The paper said that while the identity of the suspect was not revealed, voices could be heard discussing plans for the arrest and the possible need to inform Prime Minister Malcolm Turnbull and opposition leader Bill Shorten.
One voice said police are “not going in all guns blazing, it’s only half-a-dozen people and a forensic van”, it reported.
- US defector’s extraordinary N Korea love story
- Nine charts which tell you all you need to know about North Korea
The AFP said the issue had been referred to its security teams for review, and that it was making no further comment.
“Steps have been taken to ensure such incidents will not occur again,” said the spokesperson.
Mr Choi was born in South Korea but lived in Australia for more than 30 years and was a naturalised citizen.
Police allege he discussed the sale of ballistic missile technology with foreign entities, and brokered the sale of commodities such as coal, in order to raise income for North Korea.