Sound waves/vibrations move matter in the form of air particles which is how sound propagates, so that could be an exception to the rule. However, you could say water waves move matter too. They certainly don't go through matter like radio waves. Solar winds may be an exception too. They are a continuous flow of solar plasma/magnetohydrodynamic waves mixed with shock waves Hence, solar sails are possible.
. It's getting more probable that matter is made of quantum waves that act like solid particles, but aren't. Mass is energy, not matter. But it creates what we consider matter: an object that takes up space and has mass. Most waves have mass, like water or sound waves or solar wind waves. Each carries and therefor moves matter. But the matter it moves through isn't carried away by most waves.
So I don't think it's a valid rule unless it specifies the type of wave or waves we're talking about and the specific context of the rule in relation to those specific waves. If that's done, there is no exception to the rule. Otherwise, if we say there are exceptions, then the rule would be shown to be false stated simply: waves don't move matter. There's so much more to it, including the fact that the word matter is vague at best. A water wave or a shock wave hitting matter certainly can move it even if it doesn't carry it away. So, again, worded as it is, it's not much of a rule.
So, is it true that no waves move matter? No. So if it's true, then the rule has to be modified to explain the context/conditions in which it is true. Once context is specified, there are no exceptions.