The owner of a gelato shop in Melbourne has slammed the "racist coward" who left him and his wife disturbing note with a racist slur.

When Andrew arrived at his Paradise Gelato store in Cheltenham on Monday he noticed that a small note had been slipped under the door.

He quickly realised the disgusting letter was targeted at his fiance Joyce, who is of Asian descent.

"Asian Gelato. No way, go back to where you came from slopeheads," the note read.

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Andrew posted a photo of the note to Facebook, calling out the scumbag who wrote it.

"This morning we received our very first love letter from a racist coward," he wrote.

"School yourself before you drop off a note like this in our shop! The Asians who work here, one of them is a volunteer teaching assistant who wants to teach English in Japan and the other speaks 7 languages and can communicate with 70% of the world, what have you done with your life?

"If it offends you so much, kindly don't come in, it's as simple as that. No need to spread hate!"

The note was reportedly given to the police.