Monday's violence in the central Indian city damaged many vehicles and injured several people, among them at least 15 police personnel, one of whom was in serious condition, a police officer said, speaking on condition of anonymity.
Devendra Fadnavis, chief minister of the western state of Maharashtra, where the city is located, criticised the violence in a video message, calling for every effort to maintain law and order.
"I have told the police commissioner to take whatever strict steps are necessary," Fadnavis said on Tuesday.
Police said that members of the group, the Vishva Hindu Parishad (VHP), burnt an effigy of the Emperor Aurangzeb and his tomb as they chanted slogans demanding its removal from the nearby city of Aurangabad.
The police officer told Reuters the situation escalated after several members of Muslim groups marched near a police station and threw stones at police.
The attackers, wearing masks to hide their faces, carried sharp weapons and bottles, a resident of the area told the ANI news agency, in which Reuters has a minority stake.
The VHP denied accusations of engaging in any violence.
It wants the tomb to be replaced with a memorial for rulers from the local Maratha community, its general secretary, Milind Parande, said in a video message.
Nagpur is also the headquarters of the Rashtriya Swayamsevak Sangh (RSS), the ideological parent of Prime Minister Narendra Modi's Bharatiya Janata Party.
The VHP belongs to the same family of organisations.
Modi's critics have often accused him of discriminating against Muslims, and failing to act against those targeting them.
He and his government have denied the accusations.
