This was fun researching and theorizing. Thanks for asking.

We experience brain freezes when a sharp temperature drop comes into contact with the roof of the mouth and back of the throat, causing the blood vessels to constrict, which in turn causes the arteries in the brain to expand. It isn’t exactly clear where the “pain” comes from though; it is theorized that the arterial wall’s expansion triggers the trigeminal nerve (relays sensory info between face and brain) and is registered as a pain sensation.

Shark anatomy is entirely different in structure, such as they don’t have the same complex nervous system. Also, considering they are ectotherms, their body responds in completely different ways to changes in temperature than we do.

So considering what we know about shark physiology and the current theory on the mechanics behind “brain freezes”, probably not.