The video, recorded by one of the students from Maribyrnong College in the southern city of Melbourne, has been viewed almost 60,000 times after it was posted on Facebook on Tuesday with the caption "simply racism".
"These guys (security guards) are just a bit worried about your presence in our store," an Apple employee at the Highpoint Shopping Centre store is heard saying in the footage.
When one of the high school students asked why they would steal something, the employee said, "end of discussion, I need to ask you to leave our store".
Apple Australia confirmed today that the store's manager had apologised to the students and their school principal Nick Scott when they returned to the shopping centre yesterday.
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Scott said it was not the first time his students, who were at the mall dressed in school uniform, were treated in such a manner.
"They were just six kids standing around a table looking at phones," Scott told Melbourne's Herald Sun newspaper.
"At Highpoint (shopping mall) two weeks ago they asked to try out some self-propelled scooter and the guy told them, 'No, you can't, legally I can't let you try it out'.
"They walked away and turned around and another kid was using it."
Scott told AFP some of the six boys were born in Australia, and had parents who were migrants or refugees. The school itself is located in one of the poorest and most multicultural suburbs in Melbourne, he added.
Scott said he accompanied the students to the store as they were worried, as buyers of Apple products, that they would be banned from the store.
The US technology giant has a message from chief executive Tim Cook about diversity on his website, where he writes: "We want every person who joins our team, every customer visiting our stores or calling for support to feel welcome.
"We believe in equality for everyone, regardless of race, age, gender, gender identity, ethnicity, religion, or sexual orientation.