I spent over 15 years in the Medical Device field writing control software for medical instruments and as a result had to be trained & certified annually in Good Manufacturing Practice and Quality Procedures.
Yes, you could use an Arduino in a Medical Device, but I have no idea why you would want to. Since you do not have control over the Arduino's Design History, then, per FDA regulations you will have to do 100% validation testing on all the units. If you designed and built them yourself, then you could validate the design and the manufacturing process ONCE and then you only need to do final tests on the end product after manufacturing them using the validated process. Either way, the cost of doing this will vastly overshadow any minor cost benefit of buying an Arduino.
You can use an AVR, etc. chip in your device. It does not have to be "certificated" for the application. You, as the device manufacturer, are taking on that responsibility of validating that it is appropriate for the intended use. If the chip has to have a certain parameter meet a specific requirement, then you'd work with the manufacturer to be sure that all the chips you buy have that. You need to manage your supply chain, which is just not happening if you're buying Arduinos on eBay!
Sorry, but if you're at a point where you're asking such basic Quality Management questions, I strongly suggest you hire a consultant ASAP.
PM me if you need a bit of guidance. I'm no expert consultant, but at least I have experience in the field.