It is the duty of every Muslim to help his fellow Muslim brothers and sisters by means possible. Muslims in their kindness and sympathy resemble one entity and one body. That is why a Muslim is encouraged to give zakah and sadaqah to those relatives who are in need and are really eligible to receive zakah.
Dr. Nasr Farid Wasil, former mufti of Egypt states the following: Allah Almighty says, (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 wayfarers.) (At-Tawbah 9: 60) This noble verse designates the legal channels of zakah, determining them in these eight legal recipients. Moreover, the channel “for the cause of Allah” is not limited, and Allah Almighty has let it be unconditional to indicate that whatever is included under “Allah’s cause” is permissible to be provided for from the zakah.

If a parent is rich enough to afford the treatment of their child, then they are to provide for that from their own money; hence, the sick person is not entitled to receive the money due as zakah from his/her relatives, as long as the parent’s money is enough to provide for his/her treatment. This is because, in such a case, the child is in no need of others’ money and, thus, is not included in the eight categories of zakah.
However, if the parents are not rich enough to meet the expenses of treating their child and their money has all been spent for this purpose, then it is permissible to give the child from the zakah of his/her relatives in order to complete her child’s treatment. This is because the child is then one of the eight legal recipients of the zakah.
Moreover, the child is, in this case, considered to be among the needy to whom the rich should give zakah. By doing so, it would be a fulfilment of Allah’s command to help one another in doing good and righteous deeds as stated in noble verse: (But help ye one another unto righteousness and pious duty. Help not one another unto sin and transgression.) (Al-Ma’idah 5: 2)