Do you get rejected from normal minimum wage jobs when you include your degree?

If the application form ASKS for "degree" and you leave it out, that's attempted fraud and a heck of way to make an impression on a  new employer, when they find out.  If they don't ask, don't tell; see where it gets you.

With a degree they'll know it's a high likelihood you'll hate the job or quickly find something else that pays more. Unless it's a worthless degree like half of them. If your degree is in a field that has "studies" in the title leave it off all together.

Yes, I have been rejected by employers who think I am over-qualified.  But you can overcome this by also explaining why you are seeking minimum wage jobs because there is usually a good frigging reason for it that the employer is bound to discover somewhere along the way.

The applications where you did list our degree, maybe they thought you're over qualified. Don't list your degree and see what happens, or apply for other minimum wage jobs. 

If you apply for any job you only write down what is useful to them for the job you are applyng for... so a minimial wage job, means low education/low skills...so no need to write you have a degree as they are not interested in employing someone 'just for now' as it is likely they will not remain and will be just looking for a better job elsewhere