The incident took place yesterday when the mayor was not present in her office, police said.
Most of the protesters, belonging to Upper Court, Bhujpura and Ghudiya Bagh localities, claimed water supply in their areas was totally disrupted since the past four days due to power cuts.
Most parts of the old city have been facing power cuts for nearly 12 hours a day, they alleged.
In a separate incident, protesters forced the MLA from Khair, Triloki Ram Divakar to get down from his car and accompany them to the Gonda Power Station where he was allegedly compelled to make an announcement assuring public for adequate power supply.
Mayor Shakuntala Bharti (BJP) said in a statement issued here that anger of the public on erratic electricity and water supply was understandable.
Bharti assured that since today the arrangements of diesel operated electric generators have been made at fourteen different tube well stations all over the city.