Radical Islamist rebels sacked the tomb, which was listed as a World Heritage site by the United Nations on Friday and people in the West African city fear the main library could be next.
Residents told CNN they were standing guard at potential targets and were ready to do battle if necessary. "People are angry, and for a good reason," Mayor Ousmane Halle said.
The burning of the tomb was believed to have been the work of Ansar Dine, a militant group that seeks to establish strict Shariah law in Mali and has reputed ties to al-Qaida. CNN said Ansar Dine considers the Sufi offshoot of Islam to be sacrilegious.
The militants took advantage of the upheaval following a March coup by military officers unhappy with the response to a rebellion by separatist Tuareg rebels, which include the Ansar Dine.