The Australian Federal Police is investigating itself after details of an operation to arrest an alleged North Korean agent were accidentally broadcast on social media.

AFP officers arrested a 59-year-old Sydney man on Sunday and charged him, alleging he had tried to arrange the sale of North Korean missile parts.

But days before the man's arrest, the AFP's media team broadcast a minute-long discussion on live-video streaming app Periscope of how they would manage media surrounding the event.

The Periscope clip was recorded by The West Australian - whose report included details on the timing of the arrest, and whether Prime Minister Malcolm Turnbull or opposition leader Bill Shorten would need to be briefed.