The "fleshy" bit of a fin will repair in a manner similar to the way in which your own skin will repair, provided the damage is not too severe. If the soft fin rays are damaged they will also repair in a manner similar to the way in wich human bones repair. You'll need good water quality and try some aloe vera extract. If the fin has gone completely there may be some regrowth but it will not grow back to its former size.
As an aside, some tailed amphibians can regenerate a whole limb back to its origianl size and many scientist are now looking at the cell biology behind this phenomenon in an attempt to aid in human tissue regrowth after traumatic injury.
Hope the shark gets better soon.