Iman has over seventy branches, and modesty is a branch of Iman.  

عَنِ النَّبِيِّ ﷺ قَالَ الإِيمَانُ بِضْعٌ وَسَبْعُونَ شُعْبَةً وَالْحَيَاءُ شُعْبَةٌ مِنَ الإِيمَانِ  

Faith has over seventy branches or over sixty branches, the most excellent of which is the declaration that there is no god but Allah, and the humblest of which is the, removal of what is injurious from the path: and modesty is the branch of faith.  

قَالَ رَسُولُ اللَّهِ ﷺ الإِيمَانُ بِضْعٌ وَسَبْعُونَ أَوْ بِضْعٌ وَسِتُّونَ شُعْبَةً فَأَفْضَلُهَا قَوْلُ لاَ إِلَهَ إِلاَّ اللَّهُ وَأَدْنَاهَا إِمَاطَةُ الأَذَى عَنِ الطَّرِيقِ وَالْحَيَاءُ شُعْبَةٌ مِنَ الإِيمَانِ  

Modesty is part of Iman (faith).  

سَمِعَ النَّبِيُّ ﷺ رَجُلاً يَعِظُ أَخَاهُ فِي الْحَيَاءِ فَقَالَ الْحَيَاءُ مِنَ الإِيمَانِ  

He (the Holy Prophet) happened to pass by a mass of Ansar who was instructing his brother (about modesty).  

وَقَالَ مَرَّ بِرَجُلٍ مِنَ الأَنْصَارِ يَعِظُ أَخَاهُ  

from the Prophet ﷺ that he said, "Modesty brings forth nothing but goodness."

Bushayr b. Kaʿb said: It is recorded in the books of wisdom, there lies sobriety in it and calmness of mind in it, ʿImrān said: I am narrating to you the tradition of the Messenger of Allah ﷺ and you talk of your books?  

عَنِ النَّبِيِّ ﷺ أَنَّهُ قَالَ: «الْحَيَاءُ لاَ يَأْتِي إِلاَّ بِخَيْرٍ۔»

فَقَالَ: بُشَيْرُ بْنُ كَعْبٍ إِنَّهُ مَكْتُوبٌ فِي الْحِكْمَةِ أَنَّ مِنْهُ وَقَارًا وَمِنْهُ سَكِينَةً فَقَالَ عِمْرَانُ: أُحَدِّثُكَ عَنْ رَسُولِ اللَّهِ ﷺ وَتُحَدِّثُنِي عَنْ صُحُفِكَ؟  

Modesty is a virtue through and through, or said: Modesty is a goodness complete. Upon this Bushair ibn Ka'b said: Verily we find in certain books or books of (wisdom) that it is God-inspired peace of mind or sobriety for the sake of Allah and there is also a weakness in it. Imran was so much enraged that his eyes became red and he said: I am narrating to you the hadith of the Messenger of Allah ﷺ and you are contradicting it. He (the narrator) said: Imran reported the hadith, He (the narrator) said: Bushair repeated, (the same thing). Imran was enraged. He (the narrator) said: We asserted: Verily Bushair is one amongst us. Abu Nujaid! There is nothing wrong, with him (Bushair).  

قَالَ رَسُولُ اللَّهِ ﷺ الْحَيَاءُ خَيْرٌ كُلُّهُ قَالَ أَوْ قَالَ الْحَيَاءُ كُلُّهُ خَيْرٌ فَقَالَ بُشَيْرُ بْنُ كَعْبٍ إِنَّا لَنَجِدُ فِي بَعْضِ الْكُتُبِ أَوِ الْحِكْمَةِ أَنَّ مِنْهُ سَكِينَةً وَوَقَارًا لِلَّهِ وَمِنْهُ ضَعْفٌ قَالَ فَغَضِبَ عِمْرَانُ حَتَّى احْمَرَّتَا عَيْنَاهُ وَقَالَ أَلاَ أُرَانِي أُحَدِّثُكَ عَنْ رَسُولِ اللَّهِ ﷺ وَتُعَارِضُ فِيهِ قَالَ فَأَعَادَ عِمْرَانُ الْحَدِيثَ قَالَ فَأَعَادَ بُشَيْرٌ فَغَضِبَ عِمْرَانُ قَالَ فَمَا زِلْنَا نَقُولُ فِيهِ إِنَّهُ مِنَّا يَا أَبَا نُجَيْدٍ إِنَّهُ لاَ بَأْسَ بِهِ  

Ishaq b. Ibrahim narrates this hadith of the Prophet on the authority of Imran b. Husain, like the one narrated by Hammad b. Zaid.  

عَنِ النَّبِيِّ ﷺ نَحْوَ حَدِيثِ حَمَّادِ بْنِ زَيْدٍ