Short answer
No. Wudu is recommended for sa'i but not required, so sa'i without wudu is valid with no penalty. A woman whose period starts after tawaf may still do sa'i. The four schools agree on this.
Purity is mustahabb in sa'i, not wajib. Sa'i itself is wajib in Hajj and umrah: leaving it without an excuse requires a dam. It must come after a valid tawaf.
The four schools agree on this.
Explanation
Sa'i is walking seven times between the hills of Safa and Marwah, starting at Safa and ending at Marwah. The Quran calls the two hills among the symbols of Allah. The four schools agree that wudu is not a condition for it, because the Prophet ﷺ only kept a menstruating woman from tawaf and allowed her every other rite.
- Wudu breaks during sa'i: carry on. It is good to renew wudu when convenient, but you lose nothing by finishing first.
- Period starts after tawaf: she may complete sa'i, then trim her hair, and her umrah is complete.
- Sa'i before tawaf: not valid. Sa'i must follow a tawaf.
- Breaks: resting, drinking zamzam or praying a congregational prayer between laps does not cancel the laps done.
- Wheelchair: a person who cannot walk may do sa'i in a wheelchair.
The schools differ on its rank. In the Hanafi school sa'i is wajib: missing it is made up by a dam, though doing it is far better. The Shafi'i and Maliki schools, and the Hanbali school in its main view, count it as a pillar, so Hajj or umrah is not complete without it. For the steps and the duas on Safa and Marwah, see our umrah guide.
The evidence
Quran, Surah Al-Baqara 2:158
۞ إِنَّ ٱلصَّفَا وَٱلْمَرْوَةَ مِن شَعَآئِرِ ٱللَّهِ ۖ فَمَنْ حَجَّ ٱلْبَيْتَ أَوِ ٱعْتَمَرَ فَلَا جُنَاحَ عَلَيْهِ أَن يَطَّوَّفَ بِهِمَا ۚ وَمَن تَطَوَّعَ خَيْرًۭا فَإِنَّ ٱللَّهَ شَاكِرٌ عَلِيمٌ ﴿١٥٨﴾
Indeed, as-Safa and al-Marwah are among the symbols of Allah. So whoever makes Hajj to the House or performs 'umrah - there is no blame upon him for walking between them. And whoever volunteers good - then indeed, Allah is appreciative and Knowing.
Sa'i between Safa and Marwah is a rite of Hajj and umrah.
Sahih al-Bukhari 305
Sahih... افعلي ما يفعل الحاج غير أن لا تطوفي بالبيت حتى تطهري ...
"Do everything a pilgrim does, except do not perform tawaf of the House until you are pure."
Only tawaf is excluded for a woman in her period, so sa'i does not need purity.
Where the ruling is recorded
- al-Hidaya, Kitab al-Hajj, on sa'i between Safa and Marwah. Sa'i is wajib, not a pillar, and is done after tawaf.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Hajj, sunnahs of sa'i. Purity is recommended in sa'i.
- al-Mughni (Ibn Qudama), Kitab al-Hajj, on sa'i. Purity is not a condition of sa'i.
This answer is pending review by the scholars on our team. 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.