The prime minister distanced the diaspora from a diplomatic dispute over a doctored image posted by a Chinese official of an Australian soldier threatening an Afghan child.
"We acknowledge and greatly appreciate and value the contribution that generations of Chinese migrants have made to Australia," he posted to WeChat.
"Our Chinese Australian community will continue to play an important role in ensuring we remain a successful, multicultural nation."
Mr Morrison also used the post to take a swipe at China for its reaction to alleged war crimes by Australian soldiers in Afghanistan.
"Australia's transparent and honest way of dealing with this issue is a credit to this nation and a credit to all those who serve this nation in uniform," he said.
"Where there are alleged events that have taken place that require action, well we have set up the honest and transparent processes for that to take place.
"That is what a free, democratic, liberal country does."
Australia's key intelligence allies have also criticised China for pushing its provocative and antagonistic propaganda post.
Mr Morrison has demanded an apology and warned coalition colleagues against amplifying the social media attack.
"Our work is focusing on establishing dialogue that allows us to steadily work through issues as governments," he told a party room meeting.
Meanwhile, hundreds of politicians from 19 countries are urging their citizens to drink Australian wine this December to show Chinese President Xi Jinping the world will not be intimidated by bullying.
China has slapped tariffs of up to 212 per cent on Australian wine, bringing an industry worth more than $1 billion to its knees.
Australia's agriculture and trade ministers are set to meet with the nation's peak wine body in a bid to lodge a defence against China's trade intervention.
China says Australia is unfairly dumping wine into the market, slapping huge tariffs on the products that have shaken the local industry.
Agriculture Minister David Littleproud says the government will "vigorously defend" the industry, pointing out Australian wine is the second highest priced wine in China.
Along with Trade Minister Simon Birmingham, he will meet with head of Australian Grape and Wine Tony Battaglene on Wednesday to lodge an appeal with the World Trade Organisation.
The clock is ticking, with Mr Littleproud saying they have 10 days to do so.
The minister will continue working with industry to help find new markets for Australian wine.
Mr Littleproud said Australia followed the rules of international trade.
South Australian based MP Rebekha Sharkie - whose electorate covers key wine regions - is worried about the hit on local companies, urging the government to immediately support growers.
China is furious with Australia for demanding an investigation into the origins of coronavirus, speaking out about human rights abuses, and clamping down on foreign investment and interference.
It's prompted hits on a wide range of Australian exports including coal, timber, grain and seafood with bans and tariffs.