Hackers got inside computer systems at the Bureau of Meteorology, which owns one of the nation's largest supercomputers and has links to the defence department, the Australian Broadcasting Corporation reported.
ABC did not state when the attack occurred but quoted an unnamed official as saying: "It's China."
It added that the bureau -- which provides climate information spanning Australia and Antarctic territories -- held valuable scientific research and its systems were linked to several sensitive government agencies.
China has been accused of organised hacking against the US government and private firms, and in other countries as far afield as South Africa.
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In June US officials said Chinese hackers had stolen records of millions of current and former government employees. China issued a denial.
Beijing also dismissed accusations it was involved in the Australian hack, with foreign ministry spokeswoman Hua Chunying calling the report "groundless".
"The Chinese government is strongly opposed to and cracks down on all forms of cyberattacks," she added.
A spokeswoman for Australian Prime Minister Malcolm Turnbull said the government was aware of the report but could not comment on specific cases.
The weather agency refused to confirm the report, saying on its website: "The bureau does not comment on security matters."
"The bureau's systems are fully operational and the bureau continues to provide reliable, on-going access to high quality weather, climate, water and oceans information to its stakeholders," it added.
In 2013 Chinese hackers were accused of stealing the top-secret blueprints of Australia's new intelligence agency headquarters.
Two years earlier the computers of the prime minister, foreign minister and defence minister were all suspected of being hacked in attacks reportedly originating in China.