Prohibitory orders were clamped in the areas under Belbag, Gohalpur, Kotwali, Omati, Adhartaal and Hanumantal police stations following the violence triggered by the rumours, District Collector Sanjay Dubey told reporters.
Four police personnel, including an additional superintendent of police, were injured in the stone pelting, officials said.
The situation became tense after members of the minority community gathered in large numbers at the Central Jail and pelted stones, damaging its gate and some shops in the area, police said.
Incidents of violence were reported in several places including Maal Godaam and Gorandi localities. Teargas shells were lobbed in Madha Tekari area to disperse a violent crowd that tried to block a road and hold a public meeting, police said.
Members of the minority community had earlier accused prison staff of tearing up the holy book and sought action against those allegedly involved in the incident, Jail Superintendent G P Tamrakar said.
A four-member committee, comprising community leaders and an additional collector, probed the incident and found that the allegations were untrue.
A visitor had brought the holy book for Sarfaraz, a suspected member of the banned Students Islamic Movement of India (SIMI) who is being held in the Central Jail. The visitor quarreled with prison staff who searched him though Sarfaraz denied the book was torn, Tamrakar said.