The 29-year-old Alyssa Nakken joined the Giants as an intern in the baseball operations department in 2014.
Fears of smoke from the fires disrupting the Australian Open tennis receded in Melbourne, where the main tournament was due to start on Monday.
The ministry previously only targeted the Shia organisation's military wing but has now listed the whole group after the government designated it a terrorist organisation last March.
Australia is reeling from bushfires that since September have claimed 28 lives, including two on Kangaroo Island, and razed 10 million hectares (25 million acres) of land -- an area larger than South Korea or Portugal.
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