Mice can be carriers of certain diseases, illnesses. I would get checked out if it gets inflamed or shows signs of infection but you should use Neosporin ( antibiotic ointment) on any wound from bite from animal
Of course, you have to go to see a doctor if you are bit by a mouse as it can bring any disease to you - and it's dangerous as well.
It depends on whether it was captive or wild, but they both can carry diseases of their own. If it's deep then you need to think about tetanus. I would disinfect it with hydrogen peroxide. If it seemed rabid then it's important to see a doctor. But I've been bit by my hamsters six times. I've also been bit by a snapping turtle. Though it's possible to get a disease, you don't have to worry. Just use your own judgement. You'll be able to tell if you're sick.