A barbershop owner has defended her business's men-only policy after a woman lodged an official complaint.

Star Barber owner Joy Arnott in Darwin said there was a dispute after she told the female customer she could not cut her hair.

The shop's website describes it as “Darwin’s premier Barbershop for men” and Ms Arnott said they are "pro-men not anti-women".

The complaint is under investigation by the Northern Territory Anti-Discrimination Commission.

View photos Joy Arnott (centre) has defended her barbershop's men-only policy. Photo: Facebook/ Star Barber Darwin More

“Women do not have the right to take up space everywhere, just because they are women,” Ms Arnott told The NT News.

“This is an outrageous sense of entitlement and it does not reflect what I understand the anti-discrimination act is all about or should be used for.”

In Facebook posts on Monday, the store joked they had a special on "ladies haircuts for only $1000".

The issue was discussed on Sunrise's Hot Topics and both Sam Armytage and Kathy Lipari agreed the barber "absolutely did the right thing".

"[She] wasn't qualified to do the job and said so. There's absolutely noting wrong with that," Ms Lipari said.

View photos The shops' website describes it as “Darwin’s premier Barbershop for men”. Photo: Facebook/ Star Barber Darwin More

But Ben Davis disagreed, saying the incident was discrimination.

"If she wanted to get a haircut, it's on her and they should have done it," he told the program.

This comes after a Brisbane barbershop had a similar situation and faced a possible sex discrimination claim for refusing to cut a woman's hair.

Vivien Houston went to Jimmy Rod's Barbershop at The Gap Village Shopping Centre on Friday, but says she was refused service because she's a woman.

Ms Houston says she was floored and was pursuing a sexual discrimination claim.

The barber shop chain said new lease conditions imposed by centre management mean the outlet was subject to non-compete clauses aimed at protecting the trade of ladies' hairdressers in the complex.

Those lease conditions have now been changed.