Detectives have been examining the March 16 incident, which occurred at a far-right rally in Moorabbin, in Melbourne's south-east, in the days following the Christchurch attack.

Senator Anning was criticised worldwide after publishing an anti-Muslim statement following the mosque shootings.

Teenager Will Connolly, 17, attracted international publicity when he cracked an egg on the head of the politician during the Melbourne rally.

Video footage of the incident shows Senator Anning then struck out twice at the teen, who was tackled to the ground by a group of the senator's supporters, including convicted criminal Neil Erickson.

On Tuesday morning, a Victoria Police spokesman said Senator Anning and Will had both been interviewed and the CCTV footage was reviewed.

"The 17-year-old Hampton boy has been issued with an official caution in relation to the incident. A decision has been made not to charge the 69-year-old man," she said.

"On assessment of all the circumstances, the 69-year-old's actions were treated as self defence and there was no reasonable prospect of conviction."

Police are still appealing for information about a man who allegedly assaulted Will during the scuffle. Victoria Police have released an image of the man, who allegedly kicked the teen while he was on the ground.

"While the 17-year-old boy was being held on the ground, another male has approached and kicked him in the body a number of times," a police spokeswoman said on Monday.

Senator Anning was criticised after publishing an anti-Muslim statement in response to the Christchurch attacks.

The statement blamed the right-wing terror attack, where 50 people were gunned down while praying, on an increase of Islamic immigration and stated that Muslim people were "not blameless".

The Senate last week overwhelmingly voted to censure Senator Anning for the comments.

Anyone with information regarding the wanted man can contact Crime Stoppers on 1800 333 000 or submit a confidential report at www.crimestoppersvic.com.au.