Twenty-four people were hurt in the incident late on Saturday, 12 suffering bullet injuries, as police opened fire to control rampaging mobs in Muslim-majority areas.
The violence broke out, AFP reported, after Muslims accused Hindus of burning a black flag put up to protest the destruction of the mosque by Hindu zealots in the northern town of Ayodhya 11 years ago.
Hyderabad city police commissioner RP Singh said two people were stabbed to death while another died in police firing.
“We had to open fire to control the situation as the mobs were armed with petrol bombs, swords and iron rods,” he said, adding three of those injured in the rioting were in a critical condition.
Some rioters burned down an electric transformer and tried to take advantage of the darkness to damage nearly half a dozen houses, Singh said.
Another police official, AK Khan told Reuters that an "indefinite curfew has been imposed in several areas of the city after the rioting but there has been no violence since 1am". "The situation is tense but under control."
The rioting followed a relatively peaceful dawn to dusk strike in the Muslim-dominated old city area of Hyderabad, to protest against the mosque’s demolition.
In Ayodhya, Muslim and Hindu groups staged rival demonstrations as well.
Hindu extremists want a temple
on the destroyed mosque site
Security was tightened in the city and although the hardline Hindu organisation Vishwa Hindu Parishad (VHP) called for the anniversary to be observed as a "day of valour", no incidents of violence were reported.
"We have urged the youths to take a firm resolve for construction of a Ram temple in Ayodhya", state VHP joint general secretary De Jaideep Patel said in Ahmedabad, an Indian newspaper reported.
The mosque was razed in 1993 by Hindu zealots who claimed it was the birthplace of their god, Ram.
More than 2000 people died in clashes across India as a result of the mosque's destruction.
Muslims observed the day as Kheraz-e-Akidat (day of mourning), responding to a call from the Babri Masjid Action Committee to shut all businesses as a mark of protest against the razing of the mosque.