Short answer
No. Braces that straighten crooked or crowded teeth are treatment, so they are allowed in the Hanafi school and the other schools. What the hadith forbids is filing healthy teeth to make gaps for beauty. Whitening, retainers and veneers that repair damaged teeth are also generally allowed.
Correcting a defect of the teeth with braces, aligners or similar treatment is permissible. Filing or reshaping sound teeth purely for beauty (tafalluj) is haram. Fixed braces that cannot be removed do not stop wudu or ghusl from being valid.
The four schools agree on this.
Explanation
Ibn Mas'ud reported a curse on women who tattoo, pluck their eyebrows and file their teeth to make gaps "for beauty", changing the creation of Allah. The key words are "for beauty". The scholars explain that the sin is altering a sound, normal feature to look more attractive, not treating something that is out of place.
Braces are treatment. Crooked, crowded or protruding teeth can cause pain, gum disease, trouble chewing and unclear speech. Straightening them brings the teeth back to a normal, healthy state. When a Companion lost his nose in battle and a silver replacement became infected, the Prophet ﷺ told him to make one of gold, which shows that repairing a defect is not the forbidden kind of change. The Hanafi books also allow binding loose teeth with silver wire. The four schools agree that braces are allowed.
Related questions. Clear aligners and retainers take the same ruling. Whitening that brings teeth back to a natural shade is allowed. Veneers and crowns are fine when they repair chipped, stained or worn teeth; grinding down healthy teeth only to copy a celebrity smile comes close to the forbidden filing, so talk to a mufti and your dentist first. A gold tooth for a man is covered in is gold haram for men.
Wudu, ghusl and fasting. Rinse your mouth as usual. Fixed braces and bonded retainers you cannot remove do not stop your wudu or ghusl from being valid. Take removable aligners out for ghusl so water reaches the whole mouth. For brushing while fasting, see does brushing your teeth break your fast.
The evidence
Quran, Surah An-Nisaa 4:119
وَلَأُضِلَّنَّهُمْ وَلَأُمَنِّيَنَّهُمْ وَلَءَامُرَنَّهُمْ فَلَيُبَتِّكُنَّ ءَاذَانَ ٱلْأَنْعَٰمِ وَلَءَامُرَنَّهُمْ فَلَيُغَيِّرُنَّ خَلْقَ ٱللَّهِ ۚ وَمَن يَتَّخِذِ ٱلشَّيْطَٰنَ وَلِيًّۭا مِّن دُونِ ٱللَّهِ فَقَدْ خَسِرَ خُسْرَانًۭا مُّبِينًۭا ﴿١١٩﴾
And I will mislead them, and I will arouse in them [sinful] desires, and I will command them so they will slit the ears of cattle, and I will command them so they will change the creation of Allah." And whoever takes Satan as an ally instead of Allah has certainly sustained a clear loss.
Changing Allah's creation for vanity is what Satan calls to, which is the basis of the prohibition on filing teeth.
Sahih al-Bukhari 4886
Sahih... والمتنمصات والمتفلجات للحسن المغيرات خلق الله ...
"...and the women who pluck their brows and file their teeth for beauty, changing the creation of Allah."
The prohibition is tied to changing a sound feature for beauty.
Sunan Abi Dawud 4232
Graded hasan... فأمره النبي صلى الله عليه وسلم فاتخذ أنفا من ذهب ...
"The Prophet told him to have a nose made of gold."
Repairing an injury or defect is allowed, even with gold.
Where the ruling is recorded
- al-Hidaya, Kitab al-Karahiyya, section on clothing. Allows binding loose teeth with silver, and Imam Muhammad allowed gold as well.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Hazr wa al-Ibaha, section on looking and touching. Explains that the curse in the hadith concerns changing a normal feature for beauty, not removing a defect.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.