Manjit Kaur had a racial slur shouted at her by two children as she was leaving the restaurant to go to the shops, she said on Twitter on Thursday.
"The sadness that this is still a thing grows in my mind...I get in my car and drive away..... and yes for many reasons the tears come," she wrote.
Manjit, who runs the popular Twitter account for the restaurant and its sister cafe at Leeds Market, was flooded with messages of support.
She later added: "Loads of lovely messages.... it wasn't so much the words .. it was the fact they were children."
Leeds playwright and radio presenter Nick Ahad wrote online: "To everyone who wants us to win the fight in the 'market place of ideas' - you will Never understand the pain of being called this word.
"Knowing it's happening to people as good as Manjit makes us more full of rage than anyone who hasn't been called this can Ever comprehend."
Manjit began her business by cooking Indian food for delivery from her kitchen at home back in 2010, before converting a horsebox to take to festivals and weddings with her husband Michael Jameson.
The Kirkgate Market stand opened in 2016.
The couple later raised enough money, with the help of online crowdfunding, to open their restaurant on Kirkstall Road.
Manjit said she did not want to comment further when contacted.