Wudu is not required for sa'i between Safa and Marwah according to the consensus of scholars from all four schools of jurisprudence. Unlike tawaf, where the requirement of wudhu is debated, scholars unanimously agree that sa'i is valid without wudhu. This is a significant practical relief for jamaah haji, especially during the extreme crowding and panas of Haji season when maintaining ablution is very difficult.
The evidence for this ruling is clear. Nabi (shallallahu alaihi wa sallam) told Aisha when she was menstruating: 'Do everything the jamaah haji do, but do not perform tawaf around the House.' This hadith explicitly permitted her to perform sa'i (and all other rites) while in a state of menstruation, which is a greater state of ritual impurity than minor hadath. If sa'i is valid without the major purification (mandi wajib) required after menstruation, it is certainly valid without the minor purification (wudhu).
Sheikh Ibn Baz and Sheikh Ibn Uthaymeen both confirmed that while performing sa'i with wudhu is better and more rewarding — as wudhu is sunnah for all acts of worship — it is not a condition of validity. A jamaah haji who breaks wudhu during sa'i may continue without renewing it. The Permanent Committee issued the same ruling, emphasizing that this is a matter of scholarly agreement (ijma') and there is no significant dispute on this point.