Qarchak is in the desert east of Tehran. It holds political prisoners,serious drug offenders and murderers and has been described as overcrowded. There are concerns over whether there are enough beds for all inmates.
There have been reports of coronavirus cases in the prison.
A spokeswoman for the Department of Foreign Affairs and Trade said the Iranian government said Dr Moore-Gilbert has been moved from Evin to Qarchak.
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"Dr Moore-Gilbert’s case is one of the Australian Government’s highest priorities,including for our embassy officials in Tehran,"the spokeswoman said.
"We are urgently seeking further consular access to her at this new location.
"We hold Iran responsible for Dr Moore-Gilbert’s safety and well-being.