Additional security has been deployed in the wake of the protests being carried out in different parts of the city, he added.
Police said that no was seriously injured during the protests.
Joshi was Thursday sent to Moradabad jail on 14 days' judicial custody on a charge of insulting Chief Minister Mayawati. She was booked under the Scheduled Caste and Scheduled Tribe (Prevention of Atrocities) Act.
Members of the state's ruling Bahujan Samaj Party (BSP) ransacked Joshi's house in the state capital and set it ablaze late Wednesday night.