The BoM is responsible for collecting weather data, forecasting, and distributing information to other government agencies.
It owns one of Australia’s largest supercomputers, and works closely with the Australian Department of Defence (Dod) through a linked network.
The threat may have compromised potentially sensitive DoD national security information, reported the Australian Broadcasting Corporation (ABC).
According to Reuters, the DoD declined to comment on specific cyber security incidents, citing government policy.
A statement on the BoM website said: "Like all government agencies, we work closely with the Australian Government security agencies.
"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."
Despite reports claiming that the hackers were from China, the Chinese Government has denied any responsibility.
Chinese Foreign Ministry spokesperson Hua Chunying was quoted by ABC as saying: "As we have reiterated on many occasions, the Chinese Government is opposed to all forms of cyber attacks.
"We have stressed that cyber security needs to be based on mutual respect. We believe it is not constructive to make groundless accusations or speculation."
In 2011, Chinese intelligence agencies were accused of accessing the email system used by Australian federal MPs, their advisers, electorate staff, and parliamentary employees.
The agencies claimed to have accessed the emails for more than a month by hacking into Australian Government computer systems.
The US and Japan have accused China of similar security breaches in the past.