The M&M Hair Academy displayed a poster featuring the North Korean leader, emblazoned with the words “Bad Hair Day?”.
Staff at the salon in South Ealing, west London, claim they were confronted by two North Korean officials over the marketing stunt earlier this month.
Whitehall mandarins received the letter earlier this week and are now considering a response, a spokesman said.
North Korean dictator Kim Jong-un sports a striking hairdo which is shaved around the sides and longer on top.
The salon devised the poster up to advertise an offer for men’s haircuts in April following reports that male students in North Korea were told that they must adopt the same haircut as their leader.
The reports from the highly secretive country have been called into question, after visitors said there had been no noticeable change in young men’s hairstyles, and experts on North Korea dismissed the idea.
After the officials paid a visit to the salon, manager Mo Nabbach and the North Korean embassy both reported the incident to police.
Scotland Yard said it had spoken to all parties and found that no offence had taken place.
Barber Karim Nabbach, 26, yesterday said that staff at the salon did not realise the North Korean embassy was a 10-minute walk away when they put the poster up.
Mr Nabbach said that after the police had been contacted the salon had not heard anything further from the officials.
He said: “We haven’t had any trouble since then, if anything the poster has become a tourist attraction. It was just something that had been in the news, and the North Korean officials didn’t even have the haircut.
“We always put up little offers in the window, it’s harmless. We were just making light of a bad situation in North Korea.”