Short answer
No. Istinja is only for after urinating or passing stool. If your wudu broke by passing wind, sleeping or bleeding, just make wudu; washing your private parts is not needed, and the Hanafi scholars call washing after wind an innovation. The four schools agree.
Istinja is done after urine or stool. It is not done after passing wind, and Hanafi texts call istinja for wind a bid'ah. Wudu after wind, sleep or any other breaker begins with washing the hands, not the private parts.
The four schools agree on this.
Explanation
The wudu ayah lists the face, arms, head and feet. It does not mention the private parts, and the Prophet's ﷺ descriptions of wudu begin with the hands. He said there is no wudu except from a sound or a smell, and wind requires wudu only. Istinja (cleaning the private parts) is about removing impurity after the toilet, which is a separate act.
So:
- After urinating or passing stool: do istinja, then wudu. See istinja.
- After passing wind: wudu only. Wind is not impure on the body or clothes.
- After sleeping, bleeding or vomiting: wudu only, plus washing off any blood or vomit.
- Renewing wudu when you still have it: no istinja.
- Madhy or discharge: wash the area and the spot on your clothes, then wudu.
Some people wash their private parts every time they make wudu, believing it is part of it. It is not, and in cases like wind it adds to waswasa and wastes water. If you feel dampness, sprinkling a little water on your underwear after an actual istinja helps: see doubts about wudu.
For the steps of wudu, see how to make wudu.
The evidence
Quran, Surah Al-Maaida 5:6
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا قُمْتُمْ إِلَى ٱلصَّلَوٰةِ فَٱغْسِلُوا۟ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى ٱلْمَرَافِقِ وَٱمْسَحُوا۟ بِرُءُوسِكُمْ وَأَرْجُلَكُمْ إِلَى ٱلْكَعْبَيْنِ ۚ وَإِن كُنتُمْ جُنُبًۭا فَٱطَّهَّرُوا۟ ۚ وَإِن كُنتُم مَّرْضَىٰٓ أَوْ عَلَىٰ سَفَرٍ أَوْ جَآءَ أَحَدٌۭ مِّنكُم مِّنَ ٱلْغَآئِطِ أَوْ لَٰمَسْتُمُ ٱلنِّسَآءَ فَلَمْ تَجِدُوا۟ مَآءًۭ فَتَيَمَّمُوا۟ صَعِيدًۭا طَيِّبًۭا فَٱمْسَحُوا۟ بِوُجُوهِكُمْ وَأَيْدِيكُم مِّنْهُ ۚ مَا يُرِيدُ ٱللَّهُ لِيَجْعَلَ عَلَيْكُم مِّنْ حَرَجٍۢ وَلَٰكِن يُرِيدُ لِيُطَهِّرَكُمْ وَلِيُتِمَّ نِعْمَتَهُۥ عَلَيْكُمْ لَعَلَّكُمْ تَشْكُرُونَ ﴿٦﴾
O you who have believed, when you rise to [perform] prayer, wash your faces and your forearms to the elbows and wipe over your heads and wash your feet to the ankles. And if you are in a state of janabah, then purify yourselves. But if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it. Allah does not intend to make difficulty for you, but He intends to purify you and complete His favor upon you that you may be grateful.
The ayah lists the limbs of wudu; the private parts are not among them.
Jami' at-Tirmidhi 74
Grading to be checked... لا وضوء الا من صوت او ريح ...
"There is no wudu except because of a sound or a smell."
Wind requires wudu, not istinja.
Where the ruling is recorded
- al-Durr al-Mukhtar with Radd al-Muhtar, Kitab al-Taharah, chapter on istinja. Istinja is not done after wind; doing so is called a bid'ah.
- Nur al-Idah with Maraqi al-Falah, Kitab al-Taharah, chapter on istinja. Istinja is for what exits from the passages with a body.
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.