It depends a lot on what kind of brain injury. I have an brain aneurysm which has been "fixed" by putting platinum coils into it (endovascular coiling). I checked with every specialist available (interventional radiologists, neurosurgeons etc.), but of course there is no previous study or experience about coiled skydivers, so nobody could give me a definite go or no-go. However, there is some info and research about coiled divers and the study did not see any reason that would justify a no-go. Therefore I decided for myself to go skydiving again. So far, no problems.
But like I said, I am no doctor and in the end it all comes down to the type of brain injury and the individual case. Asking the doc who performed the operation (if any has been done) would be the way to go.