If you still have the original box that the mirror came in, it'll make the perfect box for packing. If not, find a box that is just slightly larger than your mirror. A tight fit will ensure that your mirror will not move around inside the box during transit. This is one way to help keep your mirror in one piece. If you cannot find the right sized box, try a local moving company. They often sell boxes that are made specifically for packing mirrors and pictures.
Once you are ready to pack your mirror, use packing tape to make an X pattern over the glass. This will help keep the mirror in place, keeping it from shifting away from the frame during transit. If you are concerned about breakage, or have a large mirror to pack, you can make multiple X patterns or a star pattern with the duct tape.
When the time comes to wrap the mirror, make sure you have plenty of bubble wrap or cushy fabric on hand. You'll need to wrap the mirror completely around one or more times. The amount of times you will be able to wrap the mirror will depend on how much space you have in the box. Your goal is to create a snug fit for the mirror inside its packing box, so wrap it just enough times to create this fit. Once the mirror is properly situated in the box, be sure to close and seal all open box edges.
When the time comes to load your mirror onto the moving truck, make sure the movers do not lay it flat. A mirror must stand straight up on one of its edges. This will avoid the chance that something will land on it during transit and shatter the mirror. To help avoid mistakes, clearly write instructions on your mirror's box. This way, the movers will know to be extra careful and to stand the box straight up.