The moving object would be moving through a cloud of steam, essentially, rather than touching the water directly. Water, at say ocean temperatures, is pretty much incompressible, so it's a tall order. Small related fact: The pistol shrimp can create sonoluminescent cavitation bubbles that reach up to 5,000 K (4,700 ☌) which are as loud as 218 decibels, breaking the sound barrier in water. Speed of sound in water at 20 degrees Celsius is 1482 m/s., (2881 knots), just for comparison to current claimed achievable speeds. For instance, an asteroid impact into the ocean does no doubt cause a sonic cone quite analogous to the one generated by supersonic aircraft. Actually, this is relevant for any supersonic motion under water, if you look at it on a big enough scale. However, it would still be relevant if you could manage to keep the pressure pertubations small enough even close to the speed of sound. Tl dr, the sound barrier isn't really relevant under water, because stranger effects turn up before you ever get close to it.

As already said by Acid Jazz, this allows for a rather remarkable mode of underwater motion, which is completely unlike anything you get in air. In particular, you will readily end up with cavitation bubbles. In water, the dynamics tend to be far more violent, even well below the speed of sound. In incompressible fluids like water, this doesn't necessarily work out the same way. This is the reason the sound barrier is such a crucial limit for aircraft. The pertubation gets ever stronger, until the dynamics are completely nonlinear and you get a shock wave. Only, when something moves faster than the speed of sound, the linear wave mode obviously can't be used anymore to transport away energy, hence any disturbance (which is inevitable when something's trying to move through the air) is “trapped”. It so happens that in air, this linear solution holds up pretty well even for rather big pertubations. In that linearised form, the solution boils down to a simple wave ansatz with linear dispersion relation, i.e. The reason that the speed of sound is a well-defined quantity is that, for small pertubations, the equations which govern the fluid dynamics can be linearised.

Breaking the sound barrier