The time it takes for a loose tooth to fall out on it's own can vary and depends on how loose the tooth is to begin with.
If it's just a little loose then it may never fall out as I have a partial loose tooth that wiggles a bit and it never has fallen out and my dentist said it was okay and not to worry about it.
But if your tooth is very loose then it can take either a few days to a week or two weeks before the loose tooth falls out on it's own.
Sometimes you can wiggle the tooth back and forth with your finger or your tongue and help it work free and eventually it will fall out.
I've had a loose tooth that eventually fell out after 1 week but sometimes they can fall out sooner or take a bit longer depending on how loose the tooth is.