The Congress and the BJP demanded a fair probe into the incident and the Shiromani Akali Dal (SAD) sought dismissal of the officers.
On Sunday evening, a brawl between Sarabjeet Singh, the tempo driver, and policemen at northwest Delhi's Mukherjee Nagar went viral on social media.
In one of the purported videos, the tempo driver was seen chasing the policemen with a sword. In another video, they were seen thrashing the driver and his son with batons.
The police said the altercation between took place after the tempo driver's vehicle collided with a police van.
Eight police personnel were injured in the scuffle, the police said.
A large number of people, particularly from the Sikh community, gathered outside the Mukherjee Nagar police station on Monday night, demanding sacking of all policemen who thrashed a tempo driver, police said.
In a video from late Sunday night, an ACP-rank officer could be seen being chased by protestors. He had gone there to pacify the protestors.
The issue had taken a political turn with Manjinder Singh Sirsa, the BJP MLA from Rajouri Garden, claiming that the policemen had insulted the man by attacking his turban.
Sirsa staged a protest outside the Mukherjee Nagar police station demanding sacking of the cops involved in the incident.
Sirsa, a member of the Shiromani Akali Dal and President of the Delhi Sikh Gurudwara Managing Committee (DSGMC), along with Sarabjeet Singh also met Delhi Police Commissioner Amulya Patnaik demanding strict action against the policemen involved.
Swinging into action, the Delhi Police suspended three policemen for "unprofessional behaviour" and initiated a probe.
Cross FIRs have been registered based on the statements of the police personnel and the tempo driver, the police said.
The case was also transferred to the Crime Branch which will be probed "independently", Deputy Commissioner of Police (New Delhi) and Delhi Police spokesperson Madhur Verma said.
Joint Commissioner of Police (Northern Range) Manish Kumar Agarwal is separately conducting a detailed inquiry into the matter.
Minister of State for Home G Kishan Reddy said he spoke to Patnaik and asked him to take immediate action.
"BJP delegation led by Shri @rpsinghkhalsa ji called on me today regarding the incident under Mukherjee Nagar Police Station in New Delhi, I spoke to CP Delhi, instructed for immediate action and to submit a detailed report," Reddy tweeted.
Kejriwal, who met the man's family, said the Delhi Police's "brutality" in Mukherjee Nagar area on Sunday was highly condemnable and unjustified.
"I demand an impartial probe into the whole incident & strict action against the guilty. Protectors of citizens can't be allowed to turn into uncontrolled violent mobsters," the chief minister tweeted.
Talking to reporters later, Kejriwal said, "I appeal to the home minister and the LG to take strict action against the guilty so that no citizen is treated like this in the future."
He has been demanding full statehood for Delhi and that the state government should have the right over police and other subjects.
On Monday, the Mukherjee Nagar area, where the incident occurred, remained tensed.
The auto drivers in the area said that they would not allow the autos, Gramin Sewas and e-rickshaws to ply on the route. They forcefully dragged the passengers out of the vehicles and diverted the vehicles to another route.
However, police, along with special force, dispersed the crowd and restored the traffic situation in the area.
WATCH: Hundreds of protesters surround Mukherjee Nagar police station