Comma After Pronoun

It depends on the preceding sentence and the sentence that follows. If you expand your sentence to give more context it will be easier to determine.

If you are listing characters and are providing a short description after each of them, then this makes sense: "Fred, who likes sports, Greg, who likes acting, and me, who likes to read."

If "me, who likes to read" is the entire sentence, then it's probably better to rewrite it. The only way I can see this sentence working is if it matches the pattern I suggested above.