Additional Superintendent of Police Rajesh Mishra was among those injured.
The rally turned violent when Youth Congress workers indulged in stone pelting prompting the police to use batons and lob teargas shells to control the situation, they said.
The event was organised by Madhya Pradesh Youth Congress (MPYC) to highlight the issue of corruption. The trouble began after the event was over and MPYC workers and Congress leaders were courting arrest. Soon stone pelting broke out, forcing people to run for cover.
Deputy Inspector General (Bhopal) Yogesh Choudhary said the stone pelting began from the Congress side after its workers were prevented from marching towards the chief minister's residence.
Police used batons and fired teargas shells to control the situation. A number of police and other vehicles were damaged in the incident, he said, adding "the situation is under control now."
State Congress President Kantilal Bhuria claimed that nearly 100 Congressmen suffered injuries.
He also claimed a party worker suffered bullet injury in police firing. But police denied using bullets and said the injury may have been caused by teargas shells.
Forensic experts have confirmed that it was not a bullet injury, police maintained.
MPYC president Priyavrat Singh accused the RSS and BJP workers of creating trouble at the event. BJP spokesman Vijesh Lunawat, however, said the incident was a result of groupism in Congress.
Congress General Secretary Digvijay Singh was among the party leaders who addressed the rally.