There is nothing wrong from the Sharia perspective in giving out one portion of zakah (up to one-third) to build a clinic or a hospital to provide free healthcare to the poor, especially if in a certain place one finds that there is no one to claim zakah for the essentials of life. One of the recipients of zakah is fi sabil Allah (Arabic for: in the way of Almighty Allah; i.e. for common good for the sake of getting Allah’s rewards). Therefore, giving out a portion of zakah for this purpose can fall under this category of the recipients of zakah.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar, responded on this as thus:
The standard view of scholars of the four schools of jurisprudence is that zakah is to be given to the poor and the needy, etc., and while doing so they should have unfettered access to it; this is known as tamlik (Arabic for: taking possession of something).
However, some scholars and jurists, both of the past and the present, have argued that part of zakah can be given to institutions to facilitate promoting the cause of Islam or good works. They consider it as falling under the category of fi sabil Allah, which is mentioned as one of the categories of the
recipients of zakah as stated in the following verse.
[The alms are only for the poor and the needy, and those who collect them, and those whose hearts are to be reconciled, and to free the captives and the debtors, and for the cause of Allah, and (for) the wayfarer; a duty imposed by Allah. Allah is Knower, Wise] (At-Tawbah 9:60).
Based on this, there is no objection to giving one portion (up-to one third) of the zakah money to build a hospital for the aforementioned purpose.
The major chunk of zakah, however, should go to providing for the immediate needs of the poor and the needy.
If, however, in a given place or time, one finds that there is no one to claim zakah for the essentials of life, then it can be given to the said purpose. This is my position in light of the principles of the Sharia, as I can decipher it from my study of the sources.