If you buy a professional or over the counter mouth guard they will usually come with a case, and if you purchase multiple guards over the course of a few years it is possible to build up a collection of these hygienic storage solutions for your dental appliances.
However here is a look at some after market mouth guard cases that are available.
These would be a good option if you loose your case, need another one for travel or keeping in an overnight bag. They also tend to be stronger and sturdier than the ones that come with an over the counter night guard.
You can also get mouth guard cases with all sorts of different colors and decorations, take a look and see if you find something you like!