Officials say the blaze was probably started by an electrical fault, the Hindustan Times reported. The 206-year-old wooden building's interior was gutted by the blaze.
At least 20 people, including 10 police officers, were injured when large protests after the fire led to clashes.
The shrine honors Sheik Abdul Qadir Geelani, also known to Muslims as Ghaus-e-Azam and to Hindus as Kahnoow. He is especially venerated by Muslims in India and Pakistan and is the patron of the Kurdish people.
Relics of the saint were rescued from the building.
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