The popstar told Rolling Stone last month that he was "part Indian - I think Inuit or something", before adding: "I'm enough percent that in Canada I can get free gas."
In a statement, CAP national chief Betty Ann Lavallée said: "Mr Bieber's comment that Aboriginal people are entitled to free gas is simply not true.
"These kinds of remarks are another example of what Aboriginal Peoples in Canada struggle with every day. It promotes the misconception that we are somehow getting a free ride.
"His simply is not the case and we are concerned that many people may believe what he said."
She added: "We would be pleased to assist Mr Bieber, if he wishes to find out more about his heritage.
"It's important for someone to know where they come from, which helps give them a better understanding of where they are going."
National vice-chief Dwight Dorey added: "While we are not in a position to confirm that Mr Bieber is of Aboriginal descent, we can assist him through the many resources available, should he wish to trace his ancestry. We would be happy to help him in this regard.
"Given that Mr Bieber is still a young man, and unaware of the facts here, I personally don't think he should be beat up over this comment. We don't think he was trying to be malicious, or making a joke of Aboriginal issues."