Officers say they opened fire to disperse the angry mob after stick-wielding protestors attempted to force their way into a headquarters building.
However protesters claim the demonstration was peaceful apart from a handful of students who threw stones.
The violence erupted during a demonstration to protest a perceived lack of police action over the rape and murder of Zainab Ansari.
Her body was found discarded in a dustbin four days after she went missing, sparking a huge reaction on social media and a campaign demanding “justice for Zainab”.
The eight-year-old’s death is just the latest in a string of 12 similar killings in the city of Kasur, in eastern Pakistan, over the past two years.
None of the perpetrators involved in any of the incidents have been caught.
A post mortem examination revealed the child had been raped and strangled.
Her family said the police failed to take action after they reported her missing after she did not return home after a Koran class.
Chilling CCTV footage shows the young girl being led away by a mystery man, and Zainab’s family say it was relatives – not the police – who took the step of recovering the video.
Her father, Ameen Ansari, who was in Saudi Arabia on a pilgrimage when his daughter went missing, blasted police for their failure to act.
Speaking after arriving back in Pakistan, he told local media: “We will not bury Zainab until the killer is caught.
“If the police would have acted immediately, the culprit would have been caught.”
The child’s sobbing mother told reporters: “I have nothing to say, I just want justice for my daughter.”
Hundreds of thousands of people attended Zainab’s funeral prayers amid scenes of mourning and tears on Wednesday night.
Police officials have reportedly ordered the arrest of those involved in the latest riots.
The region’s law chief told the Anadolu news agency: “We request the people to calm down.
“Do not take the law in your hands.”