Question: What is the ruling regarding making tawaaf around the Prophet's chamber?

Response:
Some vistors to the al-Masjid an-Nabawee make tawaaf around the grave of the Prophet (sal-Allaahu `alayhe wa sallam) and touch the caging of the chamber and its walls and, quite possibly, they kiss it with their lips and place their cheeks upon it. All of this is a detestable innovation! Certainly, making tawaaf around other than the Ka'bah is impermissible; also, touching, kissing and placing the cheeks has been legislated for a specific place on the Ka'bah (between al-Hajar al-Aswad and the door of the Ka'bah).

So, worshipping Allaah in this way, on the walls of the chamber, does not increase a person in anything except distancing himself from Allaah.

Shaykh Ibn 'Uthaymeen
al-Bid'u wal-Muhdathaat wa maa laa asla lahu - Page 403

Taken from fatwa-online.com