My invisalign retainer broke in half and I'm not in town. Are my teeth going to shift?

Since you are still able to wear your retainer, I suggest you continue wearing it until you can get back to see your Orthodontist to have them repaired or replaced. There's small likelihood of having your teeth shift if you continue to wear them. But be sure to contact your Orthodontist’s office right away to ensure you can get in as soon as you return from your vacation so there's no delay. Have a great time on your vacation, and maybe pack more carefully next time so you don't worry!

it's unlikely for drastic movement to occur in one week. You should call your doctor's office ASAP so they can order new retainer from your previous order. This way when you're back in town, the retainers will be ready for pickup and avoids further delay.

Yes you can continue to wear your retainer.  As long as you did not warp it it will still serve the purpose of keeping your teeth aligned.  Call your dentist right away and he can have another tray made and have it ready when you get back.