Witnesses said one train was leaving Sangwangsimni station in the east of the capital when it was hit from the rear by an incoming train.
One subway car was derailed and passengers walked a short distance along the tracks to the station, YTN television said.
Many of the injuries were caused by passengers jumping from the subway cars onto the tracks, a government emergency official said.
A doctor at a hospital near the station said injured people were walking in for treatment and did not appear to be seriously hurt.
A witness who said he was a passenger in one of the trains said it rammed into a train in front of it as it approached a station. He said he saw blood on the floor of a train car.
Read MoreKorea ferry disaster exposes cosy industry ties, soft penalties
An onboard announcement initially told passengers to stay inside, but most people ignored it and forced the doors open to escape, he said.
Most those who died in the ferry sinking off the southwest coast on April 16 were schoolchildren who were told by the crew to stay inside the vessel, even as the crew left.
The sinking and the deaths of hundreds of schoolchildren has hit President Park Geun-hye's approval rating.
A Gallup Korea poll issued on Friday showed her rating had plunged by 11 percentage points in the past two weeks to 48 percent.