Police said it happened in the Logan Square neighborhood's 2700-block of North Lawndale Avenue around 7:30 a.m.
After an argument, five people were trying to leave the area in a vehicle, police said. But someone began firing at them, and one suspect tried to block the vehicle from leaving.
Police said the vehicle struck one of the suspects, who was taken to Illinois Masonic Hospital in critical condition.
The Chicago Fire Department treated people who were inside the vehicle on the scene. How they were injured was not immediately clear.
One person is in custody with charges pending.
Area Five detectives are investigating. Police did not immediately provide further information.