Seems like a fishy problem, here! Okay that's a pun; there is a biological mechanism called the Weberian Apparatus that acts as an amplifier and resonance chamber (using the fish's swim bladder) to give fish (only a certain order; including carp and minnows) extremely sensitive hearing. From the link:
The Weberian apparatus functions by transmitting auditory signals straight from the gas bladder, through the Weberian ossicles and then straight into the labyrinth structures of the inner ear. The structure essentially acts as an amplifier of sound waves that would otherwise be only slightly perceivable by the inner ear structure alone. With the added function of the swim bladder as a resonating chamber, signals are amplified to noticeable levels.
In short these fish have a second route to the inner ear, one which humans (and most other fish) do not have, which give them extremely sensitive hearing.
The apparatus consists of four parts, from the posterior (swim bladder side) to the anterior (inner ear side) they have the whimsical names of the tripus, intercalarium, scaphium and claustrum. The tripus connecting to the bladder is fairly large; the intercalarium small and thin (pencil shaped), and the scaphium is medium sized (relative to the others, they are all extremely tiny in absolute terms, in the ear of a minnow). These are connected by ligaments.
A fairly minor alteration, the addition of a small voluntary muscle, could pressurize (push against) one of these first three bladder-side components to absorb vibrations, and make this channel "deaf". I think the long thin pencil shaped intercalarium would be a good bet.
Or if you prefer, have the muscle work the opposite; when relaxed it rests against the intercalarium and absorbs vibrations amplified by the bladder; when energized it pulls away from the intercalarium and gives the alien super-hearing.
I don't think you need to make the alien aquatic in any way (any more than humans are aquatic; I mean we did have a fish ancestor hundreds of millions of years ago and still have some "inner fish" biological remnants, see Your Inner Fish).
This may be just something preserved from their particular evolutionary path because in their environment, super-hearing proved useful (perhaps for hunting very quiet animals, or evading very quiet predators). They may not have a swim bladder anymore, but instead it evolved into a tiny pinhead size amplifying sac in their head and near their inner ear, which they can activate at will.