Mt Eden was formerly run by private operator Serco, but now back in the hands of the Government after its contract was terminated.
The prison's director, Dennis Goodin, said he became aware of "several" guards discussing an offender on Facebook on Friday.
"These officers have been placed on special leave pending a full investigation," he said.
The Herald has not see the post, which has since been deleted.
Goodin said all Corrections staff were expected to act with the utmost integrity and professionalism and must abide by the Department's Code of Conduct.
"Any staff found to have fallen short will be dealt with appropriately," he said.
Last week Serco agreed to pay $8 million to Corrections to cover the costs after its chief Ray Smith invoked a step-in clause in the Crown's contract with Serco, taking back management, and the cost of settling performance notices.
The multinational outsourcing group is awaiting the outcome of a judicial review into reports of its management of the facility, which was terminated after reports of organised fights and contraband surfaced on social media.
Serco took over the management of the Mt Eden remand prison in 2011 after winning a $300 million, 10-year contract.
The Corrections Department earlier confirmed that Serco's contract at Mt Eden would not be renewed. It would hand over control of the jail at a "breakpoint" in its contract in March 2017.