A staff member can be heard saying security are concerned that the boys will shoplift.
Apple said the store manager apologised to the boys, who are all black, and their school principal.
The student who filmed the video, Francis Ose, said on Facebook: "Simply racism - made them apologise tho (sic)."
Another of the boys involved, Mohamed Semra, later said on Facebook that they were satisfied with the response from Apple.
"They apologised, so we`re chilling, no need to take it further," he wrote.
The video of the incident has been viewed more than 39,000 times on Facebook.
In it, a staff member can be heard saying: "These guys are … just a bit worried you might steal something".
When the boys protest, the staff member tells them: "End of discussion - I need to ask you to leave our store."
All of the students in the video are in Year 10 and attend Maribyrnong College in Melbourne.
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