Tui was confronted by the fan following the Wallabies' 23-19 Rugby Championship loss to Argentina on the Gold Coast on Saturday. The 21-year-old has told team mates and coach Michael Cheika he was unlikely to play again this year.
"Wallabies team management have been in dialogue with Lukhan since the incident and he has indicated that he does not wish to pursue the matter any further," Rugby Australia Chief Executive Raelene Castle said in a statement on Monday.
"Therefore no further action will be taken by Rugby Australia.
"This incident was not something you want to see at any sporting event," she added.
"Emotions were running high after the match on Saturday night and I understand why Wallabies fans are frustrated after a result like that."
Castle said that two fans had managed to get into an area where players' families were seated and had been "using offensive language in criticising players".
Tui had reacted after one of his family members had been "physically caught up" in the exchange, she added.
Local media had reported that Tui's sister had been pushed.
The Queensland Reds loose forward played on Saturday despite the sudden death of his stepfather earlier in the week.
Castle said Rugby Australia would review security measures in light of the incident.
"The interaction between players and fans is an extremely important part of sport and we never want to see an incident like this again," she said.
"We feel that this is an isolated incident and we haven't experienced anything like this in our game in the past, so we don't want to race into any hasty measures."
The Wallabies, who are bottom of the Rugby Championship, next travel to Port Elizabeth to face South Africa on Sept. 29 before taking on the Pumas in Salta on Oct. 6.
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
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