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 wudu is debated, scholars unanimously agree that sa'i is valid without wudu. This is a significant practical relief for pilgrims, especially during the extreme crowding and heat of Hajj season when maintaining ablution is very difficult.
The evidence for this ruling is clear. The Prophet (peace be upon him) told Aisha when she was menstruating: 'Do everything the pilgrims 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 (ghusl) required after menstruation, it is certainly valid without the minor purification (wudu).
Sheikh Ibn Baz and Sheikh Ibn Uthaymeen both confirmed that while performing sa'i with wudu is better and more rewarding — as wudu is recommended for all acts of worship — it is not a condition of validity. A pilgrim who breaks wudu 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.