The protesters set fire to a police booth, a DTC bus and many other vehicles in Mayur Vihar phase-III, police and witnesses said.
While police refused to say if the man was killed in the police firing, residents insisted it was so.
Police said that the two-wheeler was stopped at the check point as both riders were not wearing helmets.
They were drunk and fled when a traffic policeman tried to stop them. They also indulged in an argument with the policeman, said a police officer.
A witness, however, said when the vehicle did not stop at the check point, a traffic officer threw a stick at them, which hit them and making them fall on the road.
One of the two injured was identified by police as Kamruddin, in his 20s, who was in critical condition at Lal Bahadur Shastri hospital.
The police officer said a mob collected at the spot and started pelting stones at the police team. They also set a DTC bus, a mini truck, a car, three bikes and the police booth on fire.
Police said that they had to fire shots in the air and use tear gas to restrain the crowd.
Following the incident, around 20 companies (1,600 men) of Delhi Armed Police have been deployed in and around the Mayur Vihar area, across the Yamuna, while thousands of people are still out protesting on different places.
To avoid further tension, roads to the area have been blocked by police and pickets set up every 500 metres. Ambulances and fire tenders have been stationed for any emergency situation.
Police said the situation was under control after midnight.