Are there any halachic problems with a Jew being a professional boxer?
Aside from the fact that most prize fights are on Friday or Saturday night (often before Shabbos is out), I'm not sure there is a problem. Chabad apparently doesn't think so as they have heavily promoted one of their own, welterweight fighter Dmitriy Salita (35-1-1), since he became frum and turned pro 12 years ago. (He's fighting former champion Hector Camacho Jr. in April in Brooklyn in a Showtime televised event.)
Another fighter, former WBA light middleweight champ Yuri Foreman (29-2), is reportedly learning for smicha at the Iyyun Institute yeshiva in Brooklyn (under Rabbi Dov Ber Pinson) while he trains. I think that Rabbi Pinson is also Chabad (although I'm not sure).
However, there is a general prohibition -- subject to exceptions -- to inflict a wound on someone or one's self, and even if one did not inflict a wound, to hit someone in a hostile manner is a Torah prohibition. Rambam, Hilchot Chovel U'Mazik 5:1.
Citing this Rambam, Rav Moshe Feinstein held that the mitzva "V'Ahavta L'Reyacha Kamocha" (Love your neighbor as yourself) would allow you to wound someone with his consent and for his benefit. Iggrot Moshe, Choshen Mishpat 2:66. Citing Bava Kama 91(b) (walking through thorns with uncovered legs to preserve clothing); Sanhedrin 89 (interpreting I Kings 20:35-36) and Sanhedrin 84b (permitted to perform blood-letting on father), Rav Moshe held that a girl could undergo plastic surgery because it would have a beneficial effect. Accordingly, one could arguably cite this psak as a basis to permit prize-fighting since the two fighters consent to be injured so they can make money, although that would still leave open the question of whether the risk of permanent injury warranted the gain of any amount of money.