The European Council for Fatwa and Research states that: “According to a juristic rule in Islam stating “Taking a lawful act as profession is permissible, save what’s made exceptional by a clear proof”, sport is basically permissible in Islam, if not obligatory. The Prophet, peace and blessings be upon him, urged his followers to practice some sort of sport and exercise that help keep the body fit, as long as that it doesn’t entail harm.
As for boxing, it is permissible if it’s taken as a mere hobby to train oneself on how to practice this sport, without taking a human being as a target (i.e., one should direct the fists to a punch bag and not to a person). But, one should not think of adopting it as profession. This is not permissible, due to the great harm and untold risk it involves, especially to the body and life of the victim. Islam never allows inflicting harm on any person; Muslim or non-Muslim. This is based on the juristic rule: “There should be neither harm nor reciprocating injury”.
Besides, boxing entails directing blows to the head and face. This is forbidden in Islam, according to the Hadith of the Prophet, peace and blessings be upon him: “If anyone of you fights (or, in another version, beats) a person, he should not hit him in the face.” (Agreed upon by Al-Bukhari and Muslim)