Mr McLean (21) was performing outside the Scottish Shop in George St on Monday with a busking permit and the store's permission when a noise control officer told him to move.
The incident has angered Dunedin city councillor Kate Wilson, who asked Mr McLean to perform at the council's public forum in the Edinburgh Room next Wednesday in the hope it would convince other councillors to review the noise control bylaws.
"I asked him to play so council members can hear him and appreciate the quality. But also, they can hear him tell them why it is important for the city that he continue to play.
"I was rather aghast to hear the council say that 'bylaws are bylaws' and Simon was asked to stop playing. We need to see if we can review these bylaws."
Mrs Wilson said council had spent much time and money promoting the Scottish heritage of Dunedin by employing pipers to play for tourists in the Octagon at times like Scottish Week.
Yet the good work could so easily be undone by one person, she said.
"You get one side of council promoting one thing and the other side pushing another point. It's a sad indictment on the city."
However, the suggestion that Mr McLean play in the Edinburgh Room during the hearing did not meet with Mayor Peter Chin's approval.
Mr Chin, an accomplished musician in his own right, who is supportive of pipe music in the city, said he did not believe the impromptu performance was wise.
"If he is going to play in that confined space, it might be worth checking what the decibel rating is. I would think the bagpipes would create a huge volume of noise in the enclosed space and, if that's the case, I'm not sure how that might promote sympathetic ears."
Mr McLean has placed a petition at the Scottish Shop and Farry's Menswear asking Dunedin residents to support the playing of bagpipes for 30 minutes in one area at a time in the city.