Hadith: The Prophet (may Allah's peace and blessings be upon him) forbade eating the flesh of domestic donkeys and permitted that of horses.

عن جابر بن عبد الله رضي الله عنهما : (أن النبي صلى الله عليه وسلم نهى عن لحوم الحُمُرِ الأَهْلِيَّةِ، وأَذِنَ في لحوم الخيل). ولمسلم وحده قال: (أكلنا زمن خيبر الخيل وحُمُرَ الوَحْشِ، ونهى النبي صلى الله عليه وسلم عن الحمار الأَهْلِيِّ). عن عبد الله بن أبي أوفى رضي الله عنه قال: (أصابتنا مجاعة ليالي خيبر، فلما كان يوم خيبر: وقعنا في الحُمُرِ الأَهْلِيَّةِ فانْتَحَرْنَاهَا، فلما غَلَتِ بها القُدُورُ: نادى مُنَادِي رسول الله صلى الله عليه وسلم أن أَكْفِئُوا القُدُورَ، وربما قال: ولا تأكلوا من لحوم الحُمُرِ شيئا). عن أبي ثعلبة رضي الله عنه قال: (حَرَّمَ رسول الله صلى الله عليه وسلم لحوم الحُمُر الأَهْلِيَّةِ).
[صحيح] - [حديث جابر -رضي الله عنه- متفق عليه. الرواية الثانية لحديث جابر -رضي الله عنه- رواها مسلم. حديث ابن أبي أوفى -رضي الله عنهما- متفق عليه. حديث أبي ثعلبة -رضي الله عنه- متفق عليه]

Jābir ibn ‘Abdullāh (may Allah be pleased with him) reported: The Prophet (may Allah's peace and blessings be upon him) forbade eating the flesh of domestic donkeys, and permitted eating horseflesh. Muslim's narration reads: "We ate horse meat and wild donkeys during the time of Khaybar, but the Prophet (may Allah's peace and blessings be upon him) forbade us from eating the flesh of domestic donkeys." ‘Abdullāh ibn Abu Awfa (may Allah be pleased with him) reported: We were afflicted with severe hunger during the nights of Khaybar. On the day of the battle of Khaybar, we came across some domestic donkeys and we slaughtered them. While being cooked in the pots, the Prophet's announcer called that the pots should be turned over - and perhaps he said: "And eat nothing of the donkeys' flesh." Abu Tha‘labah (may Allah be pleased with him) reported: The Messenger of Allah (may Allah's peace and blessings be upon him) prohibited eating the meat of domestic donkeys.
[Authentic hadith] - [Narrated by Muslim - Narrated by Bukhari & Muslim]

Explanation

Jābir ibn ‘Abdullāh (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) prohibited eating the meat of domestic donkeys, and permitted eating the meat of horses and wild donkeys. Moreover, ‘Abdullāh ibn Abu Awfa (may Allah be pleased with him) reported that they were afflicted with severe hunger during the Battle of Khaybar. So, after conquering Khaybar, they slaughtered some of its domestic donkeys and cooked them. After they had cooked the meat, the Prophet (may Allah's peace and blessings be upon him) ordered them to turn over the pots and not to eat from that meat.