The building suffered damage while demolishing an adjacent building near the famous Sri Meenakshi Temple, over which AIADMK leader Chelladurai claims ownership.
The heritage building houses some government offices, including that of the Public Works Department.
Police said one dome of the building and pillars had been completely damaged.
Police who received the complaint late last night said today cases had been registered against Chelladurai under various sections of the IPC.
Corporation Commissioner Nanda Gopal said Chelladurai had stated that he had purchased an old building near the heritage structure and had damaged the heritage building 'by accident'.