Footage showed the young man cracking an egg on Fraser Anning's head before the teenager was punched in the face by the senator.
A 17-year-old, who has not been identified by authorities, performed the egging during a Saturday event in Melbourne.
The encounter occurred a day after the massacre at two New Zealand mosques left at least 49 people dead and dozens injured.
Anning was speaking to media and reportedly talking about "fake refugees" and the "threat of immigration" when the violence broke out.
"Does anyone still dispute the link between Muslim immigration and violence?" he wrote.
'However, whilst this kind of violent vigilantism can never be justified, what it highlights is the growing fear within the community, both in Australia and New Zealand, of the increasing Muslim presence'.
An online fundraising page is collecting donations to pay for the teen's legal fees and to buy "more eggs".
An unnamed young man threw an egg at Anning during a press conference in Melbourne. "Let us be clear, while Muslims may have been the victims today, usually they are the perpetrators".
Mr Morrison said the government will lead a motion of censure against Senator Anning in parliament.
The attacks were perpetrated by an Australian who appears to have white nationalist views.
The Queensland senator has previously faced criticism for proposing legislation that would have restricted non-European immigration and banned Muslim migrants and for referencing Nazi policy by touting a "final solution to the immigration problem".
This isn't the first time Anning's comments have been received with condemnation and outrage.
Another posted: "I want to marry egg boy".
Opposition leader Bill Shorten voiced his anger at Mr Anning, saying he was "chasing a headline".
Multiple people were killed in mass shootings at two mosques full of people attending Friday prayers, as New Zealand police warned people to stay indoors as they tried to determine if more than one gunman was involved.