“There is no charity due upon a Muslim for his slave or his horse.”

Narrated by al-Bukhārī (no. 1463) and Muslim (no. 982), with the wording being his, from the ḥadīth of Abū Hurayrah—may Allah be pleased with him.
Muslim added: “except the charity of fiṭr.”
The wording of al-Bukhārī is: “There is no charity due upon a Muslim for his slave or his horse.”
And it was narrated by Abū Dāwūd (no. 1594) with the wording: “There is no zakāh on horses or slaves, except the zakāh of fiṭr upon slaves.”
Authenticated in Ṣaḥīḥ al-Jāmiʿ (no. 5412) and Silsilat al-Aḥādīth al-Ṣaḥīḥah (no. 2189).

Brief Explanation of the Hadith

Allah has prescribed zakāh and made it a due right upon specific types of wealth, not upon every form of property. Among this is his statement—may Allah’s peace and blessings be upon him—“There is no charity due upon a Muslim for his slave or his horse,” meaning that there is no zakāh due on slaves kept for service, nor on horses prepared for riding and personal use, because such items are not among wealth that grows and develops, upon which zakāh is obligatory.
However, if the slave or the horse is prepared for trade, then zakāh becomes obligatory upon it in that case, as it is considered part of trade merchandise, provided that the niṣāb is reached and a lunar year has elapsed.
And in the ḥadīth there is an indication of the ease of the Sharīʿah, and that zakāh is not obligatory on property acquired for personal use; rather, it is obligatory only on that in which the meaning of growth is realized. By analogy with the horse and the slave, everything a person owns for use rather than for trade—such as houses, vehicles, and the like—carries no zakāh, unless one intends them for trade, in which case they become trade goods and zakāh becomes obligatory upon them subject to its conditions.
And in the ḥadīth there is an indication that a slave does not possess independent ownership in a complete sense.
It also demonstrates the ease of the Sharīʿah and its consideration for wealth owners, by not obligating zakāh upon wealth that does not grow, which is a manifestation of facilitation and the removal of hardship from them.