Praise be to Allah.
A brother is obliged to spend on his sister if she is poor and he is independent of means and he would inherit from her if she died. If he would not inherit from her because she has a son or because the father or grandfather (father's father) is still alive, then he is not obliged to spend on her and it is permissible to give her the zakaah of his wealth in that case.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (8/169):
In order for maintenance to be obligatory, three conditions must be met:
(i)They should be poor and have no wealth or source of income which would make them independent of being maintained by others. If they have enough wealth or income to make them independent of means, then it is not obligatory to spend on their maintenance.
(ii)The one who is obliged to spend on their maintenance should have enough to do so, surplus to the costs of his own maintenance, either from his wealth or his income. If he does not have any surplus, then he is not obliged to do anything, because of the report of Jaabir that the Messenger of Allaah (blessings and peace of Allaah be upon him) said: “If one of you is poor, then let him start with himself. If he has any surplus, then let him spend on his dependents, and if he has any surplus, let him spend on his relatives.”
(iii)The one who spends should be an heir, because Allaah says (interpretation of the meaning): “And on the (father’s) heir is incumbent the like of that (which was incumbent on the father)” [al-Baqarah 2:233]. And because there are ties of kinship between those who would inherit from one another which dictate that the heir is more entitled to the wealth of the one who leaves it behind than anyone else, so by virtue of the ties of kinship he is to be singled out for maintenance rather than anyone else. If he is not an heir, then he is not obliged to spend on his maintenance. End quote.
Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti’ (13/503):
The basic principle in our view is that it is essential that the one who spends be an heir of the one on whom he spends, except for direct ascendants and descendants, in which case the issue of inheritance is not a condition. End quote.
Based on this, if the brother is obliged to spend on his sister, it is not permissible to give the zakaah of his wealth to her, but if he is not obliged to spend on her, it is permissible to give the zakaah of his wealth to her, and indeed that is better than giving it to someone else who is not one of his relatives, because by doing this he will attain the reward of both zakaah and upholding the ties of kinship.
And Allaah knows best.