"Whilst this kind of violent vigilantism can never be justified, what it highlights is the growing fear within our community, both in Australia and New Zealand, of the increasing Muslim presence," he said in a statement.
Mr Morrison was one of many who took to social media to criticise Senator Anning.
"The remarks by Senator Fraser Anning blaming the murderous attacks by a violent, right-wing, extremist terrorist in New Zealand on immigration are disgusting," he said.
"Those views have no place in Australia, let alone the Australian Parliament."
Opposition leader Bill Shorten said Senator Anning "deserves the contempt and condemnation of decent people everywhere".
"He does not speak for our parliament or our country," he said.
Former prime minister Malcolm Turnbull called the comments "contemptible".
"He is a disgrace to the Senate and what is worse by spreading hatred and turning Australians against each other he is doing exactly what the terrorists want," he said.
Greens Senator Sarah Hanson-Young drew the comparison between Senator Anning and New Zealand Prime Minister Jacinda Ardern.
"Thank goodness for the leadership and compassion of Jacinda Ardern. It is a stark contrast to the hate and ignorance of Fraser Anning," she said.
"A man of little intellect, or care. A man not fit to call himself Australian, let alone be in the Parliament."
The statement has also attracted criticism from abroad, with Piers Morgan expressing "blind fury".
Senator Anning has a history of making divisive remarks.
Last year in August in his maiden speech to parliament, Mr Anning called for a ban on Muslim immigration and urged a return to the White Australia policy.
He also came under fire for attending a Melbourne rally in January organised by ultra-nationalists.