Many reacted with shock when the waxwork was revealed on Thursday, leading the museum's team to decide to withdraw the replica.
The team admitted on Friday it "can do better" and said it would create a "more accurate representation".
After the decision was announced, O'Connor's brother Joseph O'Connor told RTE Radio he was "shocked" when he first saw the effigy online and said it did not look like her "at all".
"It looked nothing like her and I thought it was hideous," he added.
O'Connor had said if wanted to honour her memory then they should put up a statue of her in Dublin.
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'We are committed to creating a new wax figure'
In a statement, Dublin's National Wax Museum Plus said in response to the public's feedback: "We acknowledge that the current representation did not meet our high standards or the expectations of Sinead's devoted fans.
"We have listened closely to the reactions and agree that the figure does not fully capture Sinead's unique presence and essence as we intended."
The museum added: "Sinead O'Connor's impact on Ireland and the global music community is immeasurable, and our goal has always been to honour her in the most fitting and respectful manner.
"We deeply appreciate the public's love for Sinead and share in their admiration for her remarkable career and contributions.
"With this in mind, we are committed to creating a new wax figure that better reflects Sinead O'Connor's true spirit and iconic image.
"Our team of skilled artists will begin this project immediately, ensuring that every detail is meticulously crafted to celebrate her legacy appropriately.
"We extend our gratitude to everyone who provided their feedback and assure you that your voices are heard.
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