The singer's name is included on the scale, which features the names of various celebrities between 8 and 18 stone in place of numbers on its dial.
Cole took to Twitter to vent her disapproval of the product, worrying about the effect it might have on young girls.
Posting a screenshot of an article which described the scales, she wrote: "Shocked!!"
Cole continued: "Pls do not include me on your scale. Girls should be worried about the number on their exam page not a weight scale ffs"
Other celebrities featured include Rihanna, Gemma Collins, the Duchess of Cambridge, Queen Latifah and Khloe Kardashian.
Superdrug sparked an online backlash today (January 30) after the store's official Twitter account posted a link to an article about the product, which intended to break down "barriers" to people weighing themselves.
When contacted by Digital Spy about the outcry, the company initially maintained that the intention of the prototype was "to create debate and encourage people to ask for advice if they need it".
However, Superdrug have now announced that, due to the feedback received, they will not be trialling the product in stores.
"We've been listening to your comments and feedback throughout the day and are committed to helping people get healthier, and supporting those who want to lose, maintain or put on weight in a healthy and responsible way," Superdrug said.
"We created a prototype set of celebrity scales to move the conversation away from weight being perceived as a number, and we want to recognise that everyone is different.
"However, we've listened carefully to all our customers' comments and can assure them that the prototype celebrity scales will not be trialled in our stores."