City Superintendent of Police Chandan Kushwaha told PTI that a group of workers of AISF, student wing of CPI, and youth wing of Lalu Prasad's party came to the state BJP office to protest Kumar's arrest.
As BJP workers protested, a clash broke out in which stones and water bottles were hurled from both sides.
Police used mild force to separate the groups, the City SP said.
BJP which had sought permission to take out a march from its office to Income Tax roundabout was not allowed by the police and stopped at the party office itself.
Also Read
The City SP said the situation has been brought under control and additional police force has been deployed to prevent further clashes.
BJP state vice president Sanjay Mayukh told PTI that the event reflects the "fascist face of Nitish Kumar government."
"We had taken prior permission for taking out a march which was not permitted. The workers of AISF and RJD armed with lathis were allowed to come up to our party office and attack us without any prior notice," Mayukh said.
Kumar hails from Bihar.