All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Imaam An-Nawawi reported in his book Al-Majmoo' that Al-Maawardi mentioned that Istinjaa’ with the water of Zamzam is valid by the consensus of Muslim scholars.
However, many Muslim jurists considered it disliked to use the water of Zamzam in removing impurities, including Istinjaa’, yet they ruled that it is valid. The rationale behind considering it disliked is that the water of Zamzam is a blessed water. Ibn Al-Qayyim said: “Zamzam water is the best and noblest of all waters, the highest in status, the dearest to people, and the most precious and priceless to them. It was dug by Jibreel and it quenched the thirst of Ismaa‘eel.”
As for using the water of Zamzam for ablution and Ghusl, it is permissible without any dislike, for it was reported in Al-Musnad and was authenticated by Shaykh Ahmad Shaakir on the authority of ‘Ali ibn Abi Taalib that the Prophet, sallallaahu ‘alayhi wa sallam, “asked for a pot containing Zamzam water and drank and performed ablution from it.”
Allaah Knows best.