The Prophet ﷺ said, "There is no zakat due on a man's slave or his horse."
حدثنا عفان قال حدثنا وهيب قال حدثنا خثيم بن عراك بن مالك عن أبيه
عن النبي ﷺ قال ليس في عبد الرجل ولا في فرسه صدقة
Its chain of transmission is sahih. Bukhari narrated it with a similar wording, 2/149, in the chapter on zakat, "There is no zakat due on a Muslim for his slave," and Muslim narrated it likewise, 2/675, number 982, and Nasai, 5/35, number 469, and Abdul-Razzaq, 4/33, number 6878.