Western Sydney Jumping Castles and Face Painting took to social media on Wednesday to stress it was not involved and did not support its rival company's' posts.
"Please understand that these comments were made by another company called Western Sydney Jump," the company said.
"I'd like to let everyone know the stress and threats we've had to endure as a result of what's occurred is very sad."
Premier Chris Minns condemned the actions of Western Sydney Jump, which reportedly boasted on social media about refusing to take "a Zionist booking".
The booking request came from Masada College, an independent Jewish school on Sydney's upper north shore.
"It's not in keeping with any part of our multicultural community," Mr Minns said.
"I condemn it completely. This must be investigated by federal and state authorities."
Police were at the school on Wednesday morning making inquiries but had not launched a formal investigation.
Western Sydney Jump's Instagram page, where the post was said to have been made, and its website were offline in the morning.
Repeated attempts to contact the business owner were unsuccessful.
According to screenshots published by various media outlets, the business's owner tried to  draw a distinction between Jews and Zionists in its posts.
Executive Council of Australian Jewry co-chief executive Alex Ryvchin said the incident was sadly indicative of the surge in anti-Semitism in Australia "under the disguise of political activism."
"To refuse to hire a jumping castle to kids who happen to be Jewish is the height of prejudice and low bigotry," he said.
"The business should be ashamed."
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