As far as I know — Musa was uncertain — the Prophet ﷺ performed itikaf in a tent made of palm leaves.
حدثنا عبد الله حدثنا موسى بن داود حدثنا علي بن عابس عن أبي فزارة
فيما أعلم شك موسى أن النبي ﷺ اعتكف في قبة من خوص
No references are available.
Its chain of transmission is daif because of Ali bin Aabis. Ibn Hibban, Yahya, Ibn Main, and Nasai declared him daif, while Ibn Adi said, "His hadith is written down." It is found in Tabarani 20/352, no. 830, and Haythami attributed it to them both in 3/173 and declared it daif.