Shadows and lighting are good ways to provide depth queues.
You could just stop the hands from exceeding a certain depth in code, but that might feel unnatural to your users. Maybe use a nonlinear limiting scheme so that the hands still move in depth a little bit when they are close to the plane, but never quite reach it.
You could also make the background translucent so that the user can tell that their hands are past the barrier, but can still see them.