As far as Islamic Shari`ah is concerned, it is permissible to give zakah to a poor student in order to help him complete his studies.

Dr. Monzer Kahf, a prominent economist and counselor states: It is permissible to give zakah to a student to complete his study as long as the student is poor. It is up to the poor person to use the amount of zakah given to him in the way he sees fit. There is an example of a poor woman who was given somesadaqah and she used some of it as a gift to the Prophet (peace and blessings be upon him). The student can use the amount given to him for study expenses or for any other purpose. The criterion is that he is poor when given the zakah.

Moreover, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, adds: We are allowed to give part of our zakah, but not the entire amount, to a poor student who is pursuing his essential college education. This is because in Islam everyone is entitled to an education that can help him establish a suitable career. Education is one of the basic necessities of life in the modern world, and Islam values it very highly. This is so, as long as he is pursuing a field of study which is considered beneficial for humanity.

Having said this, however, I must hasten to point out that zakah funds cannot be given to someone who is engaged in studies as a hobby, and which has nothing to do with finding a suitable career. In that case, we are best advised to direct these funds to more deserving people.

The primary recipients of zakah are those who are desperately poor or needy or those who are in debt or stranded on a journey due to lack of funds; for more details on this issue see relevant answers on this site.