A burger restaurant owned by celebrity chef Neil Perry has apologised after one of its staff members directed a racial slur at a customer in Melbourne.

Nicholas Muchinguri went to Burger Project, in Melbourne's CBD, on Friday to have lunch with some friends.

Next to the order number on his receipt, where his name should have gone, it said "n*****".

Rutendo Muchinguri said the incident showed the community still had a long way to go. ( Facebook: Rutendo Muchinguri )

"This is what happened to me at Burger Project, they said it was a 'typo'. Totally disgusting in this day and age!" he tweeted.

Mr Muchinguri's wife later took to Facebook to express her disappointment such language was being used in modern Australia.

"It is so disappointing that in a place where my husband spent his hard-earned money, he received this sort of disgracefully discriminatory treatment," Rutendo Muchinguri wrote.

"It's exhausting that in 2017, in a modern and multicultural society some of your staff remain insensitive to the impact that this insidiously nasty and vile word has.

"Come on, you can do better. This is NOT OK. I guarantee you that we will not be spending our money at any Rockpool Group businesses. I want to know what you will do about this."

Burger Project later apologies, says it fired staffer

In a Facebook post that evening, Burger Project apologised and said the staff member had been fired.

"We are very concerned to learn about the unacceptable language used by an employee of our Burger Project St Collins Lane store today," it said.

"We do not condone this kind of behaviour from our staff, or accept this treatment of our customers.

"As soon as we became aware of the matter this afternoon, when we were contacted on the behalf of the customer, we acted: we reached out and apologised and the employee's position was terminated.

"The employee's behaviour was in breach of our code of conduct and such behaviour won't be tolerated.

"We apologise profusely for the upset and hurt this has caused."

'Hopefully this is a learning experience'

But the couple said they were not contacted or given an apology by the restaurant until Saturday morning, when Perry rang her husband, not on Friday as Burger Project said on social media.

"Although we are happy to see that there was repercussions for the staff member, we don't wish him any ill will," a post on Facebook signed by both of them read.

"Hopefully this will turn into a learning opportunity for him and the entire staff at the Burger Project.

"We also want to thank Neil Perry for calling Nicholas first thing this morning to offer an apology on behalf of the company.

"We felt that the initial response of the Burger Project was more concerned about its public image than the hurt caused."

They thanked people for their support and said they felt encouraged that the majority of people saw how hurtful the situation was.

"It's concerning to see that there are some comments that perpetuate this type of prejudice and racism," they said.

"We've come a long way but there is still more to do and more conversations to be had.