Mr Morrison said the cyber attacks were targeting a “range of sectors” including “all levels of government”.
They have been ongoing for many months but the “frequency has been increasing”, he added.
Mr Morrison did not name a state actor but said there “not a large number” of countries which could be behind the attacks.
Speaking at a press conference on Friday, Mr Morrison said: “Australian organisations are currently being targeted by a sophisticated state-based cyber actor.
“This activity is targeting Australian organisations across a range of sectors, including all levels of government, industry, political organisations, education, health, essential service providers and operators of other critical infrastructure.
“We know it is a sophisticated state-based cyber actor because of the scale and nature of the targeting and the trade craft used.
“Regrettably, this activity is not new. Frequency has been increasing.”
He said that no major personal data breaches have been made.
The cyber attacks come after Australia clashed with China after demanding an investigation into the origins of coronavirus.
Beijing responded by imposing an 80 percent tariff on Australian barley.
China has also warned students and tourists not to travel to the “racist” country.
Australian Strategic Policy Institute executive director Peter Jennings said China is likely to be behind the cyber attacks.
He told The Australian: “The Russians could do it. The North Koreans could do it, but neither of them have an interest on the scale of this.
“They have no interest in state and territory government or universities.
“The only country that has got the interest to go as broad and as deep as this and the only country with the sophistication and the size of the intelligence establishment to do it, is China.”
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