More than 70 people, including 10 policemen, have been injured in the clashes since Monday when the two-centuries-old Sufi shrine was demolished by civic authorities in Baroda, 120km south of Ahmedabad, the main city of Gujarat state.
City police chief Deepak Swaroop said: "A young man has been burnt to death. The situation is tense and curfew has been imposed."
The 30-year old Muslim man, who worked in an oil refinery, was returning from a late shift when he was surrounded by hundreds of people, including activists of hardline Hindu groups linked to the Bharatiya Janata Party, which rules Gujarat.
Minority Muslim residents said they did not trust the state government.
One resident, Moyin Khan, said: "Our lives are in danger as Hindu extremists armed with swords and knives surrounded our residences. We called the police but no one responded."
Amit Shah, the state home minister, said the government was keen to control the violence and was doing all it could.
Hardline Hindu groups have a
strong presence in Gujarat
Civic authorities said they had to demolish the Muslim shrine because it was illegal and blocking a road-widening project.
Gujarat is one of India's most communally sensitive states.
The highly industrialised state was rocked by Hindu-Muslim riots in 2002 when 59 Hindus were burnt to death in a train compartment, which the state government blamed on Muslims.
Human-rights groups say about 2,500 people - mostly Muslims - were hacked, beaten or burnt to death in retaliatory attacks. Officials put the toll at more than 1,000 people.