My understanding is this:
There is no need to "shut down" Git, since Git doesn't *do* anything unless someone executes a Git command that references that repository. Or rather, you "shut down" Git by telling everybody to
not use it until you get the repository moved. However, if it is accessed remotely by people you can't easily control, you may need to shut down the access protocol's daemon to prevent the remote users from executing Git commands while you move the repository.
Moving a repository is simple: It contains no references to its absolute location. So all you have to do is move the entire directory structure to the new place.
(I'm assuming here that the repository is a bare repository.)
One question is whether there are other repositories that reference this one. In that case, you have to update the configuration information in the other repositories to point to the new location of the master repository.