In case you were wondering, you can water ski barefoot if you want to. Yet, if you are a novice, it may not be the best idea to start with it. It all comes down to your tolerance with pain, to be honest.
Yes, to answer the question, barefoot water skiing can be somewhat painful. This is especially true if the water you are riding on is incredibly smooth. Across your instep, the surface of really smooth water can create an unpleasant sensation.