Majority of scholars agreed that a husband can’t give zakat to his wife, because when he gives the zakat to his wife, then he no longer needs to give sustenance (nafkah) and abolish his obligation. So, the zakat’s benefit returns to him, as if he were paying for himself.
Ibn al-Mundhir said: They (the scholars) are unanimously agreed that a man should not give his zakaah to his wife because he is obliged to spend on her, which means that she does not need zakat. (Al-Ijma’, Ibnul Mudzir page. 51)
As for the wife to give zakat to her husband, most scholars recognize it, among them are Sufyan ats-Tsauri, As-Syafi’i, Abu Yusuf, an opinion from Malik, Ahmad and Abu Ubaid. They quote as evidence the report narrated by Imam al-Bukhari (1462) and Imam Muslim (1000) from Abu Sa’eed al-Khudri (may Allah be pleased with him):
(Meaning): On Eid ul-Fitr or Eid ul-Adha, Allah’s Messenger (Peace be Upon Him) went out to the Musalla. After finishing the prayer, he delivered the sermon and ordered the people to give alms. He said, “O people! Give alms.” Then he went towards the women and said. “O, women! Give alms, for I have seen that the majority of the dwellers of Hell-Fire were you (women).” The women asked, “O Allah’s Messenger! What is the reason for it?” He replied, “O women! You curse frequently and are ungrateful to your husbands. I have not seen anyone more deficient in intelligence and religion than you. O women, some of you can lead a cautious wise man astray.” Then he left. And when he reached his house, Zainab, the wife of Ibn Mas`ud, came and asked permission to enter It was said, “O Allah’s Messenger! It is Zainab.” He asked, ‘Which Zainab?” The reply was that she was the wife of Ibn Mas’ub. He said, “Yes, allow her to enter.” And she was admitted. Then she said, “O Prophet of Allah! Today you ordered people to give alms and I had an ornament and intended to give it as alms, but Ibn Mas`ud said that he and his children deserved it more than anybody else.” The Prophet replied, “Ibn Mas`ud had spoken the truth. Your husband and your children had more right to it than anybody else.” [Narrated by Al-Bukhari & Muslim]
It is not permissible for a husband to give his zakat to his wife because the husband is obliged to give provision of means to support his wife life even the wife is rich. However, it is permissible for the wife to give zakat to her husband because she is not obliged to give provision of means to support his husband life despite her husband is poor.