The application includes a "Bully Mode" which gives meaner insults and the ability to post "Your Ugly Photos" to Facebook and Twitter.
"That shows that bullying isn't something the developers are too concerned about," Mr Cocker said.
For children who are vulnerable to bullying, the Ugly Meter could be "particularly harmful".
"If a child is particularly concerned about their looks then while this might seem like a bit of fun, it could be quite painful for them to experience."
The low cost of the application - $1.29 - meant children could afford to download it on their own accounts without their parents knowing about it, Mr Cocker said.
"It's something that society will just have to roll with, which is a bit unfortunate."
The Ugly Meter is pitched as a means of determining how unattractive you are.
"Do you ever wonder if you're ugly and your friends just don't tell you?" it says.
Created last year, the Ugly Meter has recently leapt up the list of the Apple App Store's most popular applications after coverage by American mainstream media. It is also available on Android devices.
The Ugly Meter has been downloaded more than five million times worldwide, generating more than US$500,000 ($620,000) in revenue.
Developer Dapper Gentlemen made US$80,000 in a day after the US$4.99 Pro version was showcased on Howard Stern's morning radio show in the US, according to the Daily Mail.
Check out what the ugly meter has to say about some of the world's hottest celebrities.
