Lady Umm Salamah (may Allah be pleased with her), the wife of the Prophet ﷺ, says: I complained to the Messenger of Allah ﷺ that I was ill (and performing Tawaf on foot was difficult), so he ﷺ said: "Perform Tawaf riding on your mount, away from the people" (so that the mount does not cause inconvenience to the people). She says: I performed Tawaf on my mount, and at that time the Messenger of Allah ﷺ was praying beside the Ka'bah and reciting Surah At-Tur.
Hadith Referenceالسنن المأثورة / باب ما جاء في فدية الأذى / 479
Hadith Takhrijصحیح بخاری، الصلاۃ، باب ادخال البعیر فی المسجد للعلۃ، رقم: 464، صحیح مسلم، الحج، باب جواز الطواف علی بعیر وغیرہ، رقم: 1276۔