Television footage showed a supporter trying to grapple with Tui after Australia had fallen to a 23-19 Rugby Championship defeat at home to Argentina.
Another spectator eventually dragged the irate fan away from Tui, but it marred another disappointing performance from the Wallabies.
Australia's players wore black armbands for the match in memory of Tui's stepfather, who died earlier in the week, and Cheika explained his player became involved in the scuffle after the supporter knocked over the 21-year-old's sister.
"It's one thing being upset with a team but I think what went down there was the supporter pushed Lukhan's sister," Cheika said.
"Obviously that family has had a very big week and I don't think it's appropriate that happened.
"I get the discontent and you own that. Words, abuse, it comes sometimes and you have to suck it up when you don't play well.
"He pushed the younger sister and Lukhan didn't like that and that's fair enough considering everything that has happened to him this week.
"It got to the point where the player just said in the dressing room he's not going to be playing anymore - because of that incident.
"So I hope the fan is happy."