The device was found on HMAS Leeuwin on Sunday while it was docked in Cairns in far north Queensland, leading to the government saying Australian Defence Force personnel deserve to be safe in their workplace.
An investigation has been launched by Defence into the incident, with it being referred to the Joint Military Police Unit.
A Defence spokesman said the person of interest was assisting the military police unit with inquiries.
"Navy's focus and priority is providing support to those who are impacted by this incident," the spokesman said.
Chief of the Navy Vice-Admiral Matt Buckley said an audit of all bathroom facilities across the naval fleet was being carried out.
"This act is the most despicable betrayal of trust and is fundamentally misaligned with our values," he said in a statement.
"We will tackle this act of sexual violence with all of our energy. Any perpetrator will be held to account."
Tasmanian Senator Jacqui Lambie, who served in the army and raised the issue in the Senate, said Defence should not be left to investigate the incident in order to make sure it's properly dealt with.
"This is a culture that, unfortunately, Defence has not been able to clean up, and it hasn't even come close," she told ABC TV on Thursday.
"The only way to fix this problem is to take the legal system outside of Defence's hands.
"Their job is to fight in a war ... and they don't deal with this very well when it comes to the legal system."
Senator Lambie said since the incident was made public, others had come forward over similar incidents that occurred over recent months.
"I should tell you that I'm surprised, but I'm not which is really unfortunate. It does bother me a lot, though, with what's going on," she said.
"The only way we're going to be able to stop this is by taking it out of Defence's hands and having an independent body that actually deals with this."
Federal minister Anika Wells condemned the discovery of the recording device.
"I really feel for all of the people who are on that ship who are learning this and the people that may have been victims of this act," she told ABC TV on Thursday.
"You deserve to be safe in your workplace, and the rise of tech-facilitated abuse, particularly upon women, is horrific."
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