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The image was shared to Twitter - a website blocked on mainland China - by Zhao Lijian, a spokesman with the nation's foreign ministry.
Mr Morrison said the falsified image was utterly outrageous.
"The Chinese government should be totally ashamed of this post. It diminishes them in the world's eyes," he told reporters in Canberra on Monday.
"Australia is seeking an apology from the ministry of foreign affairs, from the Chinese government, for this outrageous post. We are also seeking its removal immediately and have contacted Twitter."
Twitter has added a content warning to the post.
But China's embassy in Australia believes politicians there had "misread" the tweet and are trying to stoke nationalism.
"The rage and roar of some Australian politicians and media is nothing but misreading of and overreaction to Mr Zhao's tweet," the Chinese embassy in Canberra said in a statement on Tuesday.
Australia's Foreign Affairs and Trade secretary had called ambassador Cheng Jingye on Monday to complain about the social media post, it confirmed, adding that Cheng had "refuted the unwarranted accusations as absolutely unacceptable".
Australia was seeking to "stoke domestic nationalism", and "deflect public attention from the horrible atrocities by certain Australian soldiers", it said.
An apology appears unlikely, with editor of Chinese-government run media outlet Global Times Hu Xijin describing the image as a "popular cartoon".
"It is a popular cartoon that condemns the Australian Special Forces's brutal murder of 39 Afghan civilians," he posted on Twitter.
"On what ground does Morrison feel angry over the use of this cartoon by the spokesperson of Chinese FM? It's ridiculous and shameless that he demanded China to apologise."
China intensified its condemnation of alleged war crimes by Australian soldiers in Afghanistan after Russia made similar comments.
Mr Morrison said there were undoubtedly diplomatic and trade tensions between Australia and China but he hoped to reset the dialogue. He suggested he had previously written to Chinese President Xi Jinping in an effort to reset relations.
The image purported to show a special forces soldier slitting the throat of an Afghan child with its head wrapped in an Australian flag, alongside the words: "Don't be afraid we are coming to bring you peace."
"Shocked by murder of Afghan civilians and prisoners by Australian soldiers," Zhao Lijian posted to Twitter. "We strongly condemn such acts and call for holding them accountable."
New Zealand's Prime Minister Jacinda Ardern said earlier on Tuesday that New Zealand has registered its concern with Chinese authorities over the use of the "unfactual" image of the soldier.
The inflammatory tweet came just days after China effectively blocked an $A1.2 billion ($NZ1.25 billion) wine export industry by imposing dumping tariffs of up to 200% on Australian wine.
Australia has said there looks to be a pattern of Chinese trade sanctions against Australian products this year, linked to Beijing's diplomatic grievances over Australia's national security, human rights and foreign policy decisions.
- AAP and Reuters