Western Sydney Jumping Castles and Face Painting took to social media on Wednesday to stress it was not involved and did not support a rival company's posts.
"Please understand that these comments were made by another company ...," it 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 cautioned Western Sydney Jump, which allegedly 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."
NSW 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 allegedly made, and its website were offline on Wednesday 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 a 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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