On the authority of ʿAmmār ibn Yāsir, that the Messenger of Allah (peace and blessings be upon him) said: "Up to the elbows."(1)

329 — ʿAbd al-Malik ibn Shuʿayb ibn al-Layth narrated to us, my father narrated to me, on the authority of my grandfather, on the authority of Jaʿfar ibn Rabīʿah, on the authority of ʿAbd al-Raḥmān ibn Hurmuz, on the authority of ʿUmayr, the freed slave of Ibn ʿAbbās, that he heard him say: I set out, I and ʿAbd Allāh ibn Yasār, the freed slave of Maymūnah, the wife of the Prophet (peace and blessings be upon him), until we entered upon Abū al-Juhaym ibn al-Ḥārith ibn al-Ṣimmah al-Anṣārī. Abū al-Juhaym said: The Messenger of Allah (peace and blessings be upon him) came toward the well of Jamal, and a man met him and greeted him with salām, but the Messenger of Allah (peace and blessings be upon him) did not return the greeting to him until he reached a wall, whereupon he wiped his face and his hands, then returned the greeting to him.(2)

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(1) Its chain of transmission is weak due to the anonymity of the narrator from al-Shaʿbī, while the rest of its narrators are trustworthy. Abān: he is Ibn Yazīd al-ʿAṭṭār, and al-Shaʿbī: he is ʿĀmir ibn Sharāḥīl.
It was also recorded by al-Bayhaqī 1/210 via the route of the compiler, with this chain.
It was also recorded by al-Bazzār (1391), al-Dāraquṭnī (693/2), al-Bayhaqī 1/210, and Ibn ʿAbd al-Barr in "al-Tamhīd" 19/286 via the route of Mūsā ibn Ismāʿīl: Abān narrated to us, he said: Qatādah was asked about tayammum during travel, and he said: Ibn ʿUmar used to say: up to the elbows, and al-Ḥasan used to say: up to the elbows, and Ibrāhīm al-Nakhaʿī used to say: up to the elbows, and a narrator narrated to me from al-Shaʿbī... and he mentioned it. In some sources, this ḥadīth was mentioned to Aḥmad ibn Ḥanbal, and it impressed him, and he said: How excellent it is.
(2) Its chain of transmission is authentic. al-Layth: he is Ibn Saʿd.
It was also recorded by al-Bukhārī (337), Muslim in suspended form (369), and al-Nasāʾī in "al-Kubrā" (303) via the route of al-Layth ibn Saʿd, with this chain. In Muslim's version: Abū al-Jahm, which is an error as stated in "Sharḥ al-Nawawī."
It is also in "Musnad Aḥmad" (17541).
His saying: "the well of Jamal" is the name of a place in Medina.