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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.
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.
The prime minister 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."
Foreign Affairs secretary Frances Adamson spoke to Chinese ambassador Cheng Jingye to relay Australia's position.