Nothing will happen. A dog will eat many dirty things. Even if its a wild mouse with diseases. My dog caught a mouse in my backyard.. All that will happen is that it will dispose of the intestines
If you have a mouse that is properly housed in a cage or aquarium, it should be safe to keep as a pet. The considerations you should look at before keeping a mouse as a pet are the following:
Mice...
Mice live in colonies and NESTS. Nests are constructed with materials collected during the search for food. Torn paper and fibers are common nesting material for mice living in contact with humans.