Hadith: The Messenger of Allah (may Allah's peace and blessings be upon him) said concerning the daughter of Hamzah: She is not lawful for me (to marry). That which is unlawful due to lineage (blood relation) is unlawful due to breastfeeding. She is the daughter of my foster-brother.

قال رسول الله صلى الله عليه وسلم في بنت حمزة: «لَا تَحِلُّ لِي يَحْرُمُ من الرَّضَاعِ مَا يَحْرُمُ من النَّسَبِ وهي ابنة أَخِي من الرَّضاعة».
[صحيح] - [متفق عليه]

The Messenger of Allah (may Allah's peace and blessings be upon him) said concerning the daughter of Hamzah: ''She is not lawful for me (to marry). That which is unlawful due to lineage (blood relation) is unlawful due to breastfeeding. She is the daughter of my foster-brother.''
[Authentic hadith] - [Narrated by Bukhari & Muslim]

Explanation

'Ali ibn Abi Tālib (may Allah be pleased with him) wished that the Prophet (may Allah's peace and blessings be upon him) marry the daughter of their uncle, Hamzah. However, the Prophet (may Allah's peace and blessings be upon him) said that she was not permissible for him, because she was the daughter of his foster-brother. Indeed, the Prophet and his uncle Hamzah were breastfed by Thuwaybah, a slave of Abu Lahab. So Hamzah became the Prophet's foster-brother, and the Prophet became uncle of Hamzah's daughter. The rule is that things that are forbidden because of birth (blood relation) are likewise forbidden because of breastfeeding.