Do external faucets have an indoor shutoff valve somewhere indoors?
Yes, typically houses in northern (freezing) climates have an indoor shut off.  When winterizing your house, you should turn the indoor valve off, and leave the outside one open so that the water can drip out.  The danger is that the water can freeze and burst the pipe.

I'd look for the shut off in the basement, on the other side of the wall where the outdoor faucet is.  Trace the pipe back until you find something.