In his strongest comments on any Chinese government action since he became Prime Minister,Mr Morrison said the image was"truly offensive"and"repugnant".
"The Chinese government should be totally ashamed of this post. It diminishes them in the world's eyes,"he said.
"It is an absolutely outrageous and disgusting slur. Australia is seeking an apology from the Ministry of Foreign Affairs and we are seeking it be removed from Twitter."
Foreign Ministry spokesman,Zhao Lijian,said in the post that he was"shocked by the murder of Afghan civilians and prisoners by Australian soldiers.
"We strongly condemn such acts and call for holding them accountable,"the post accompanying the image said.
The illustration was created by Wuheqilin,a self-styled Chinese"wolf warrior"artist,who came to prominence for his pro-Beijing illustrations during the Hong Kong protests last year.