The violence flared during a protest organised by the Tamil Nadu Muslim Munnetra Kazhagam, an Islamist movement, against an anti-Islam film which has triggered similar protests in large parts of the Muslim world.
The protesters also burnt an effigy of US President Barack Obama and an American flag, police said.
One group hurled stones, while others lifted iron barricades placed in front of the main gate to smash windows, police said.
“We have tightened the security and the situation is well under control,” JK Tripathy, the police commissioner in the southern city, told local reporters.
One of the organisers said that what had been planned as a peaceful protest was hijacked by militants.
“We wanted to organise a peaceful demonstration to express our dismay over the film, but the youngsters, who could not hold their nerves, ran and attacked the consulate office,” Gunangudi Hanifa told AFP.
A spokesman for the consulate, who did not give his name, said that no staff had been hurt in the attack.
“No one was injured and all the staff members are safe,” he said.