One train of subway line 2 ran into the back of another that stopped between stations because of mechanical problems near Sangwangsimni Station at around 3.30 p.m., Xinhua reported.
Some of the injured passengers have been taken to the nearby Hanyang University hospital.
Most of them have light ankle or feet injuries, officials said. Ten ambulances have been sent to the station, officials said.
Two cars of the train were derailed as a result of the collision and passengers walked from the trains on the tracks to the station. Officials of Seoul Metro said both trains were manually driven.
The train in front was approved to stop there for checking problems, but the back train did not keep a safe distance and rammed into the rear end of the front one after suddenly applying its brakes.