The incident happened during the morning rush hour at the Francia station, in the city centre.
Reports said the train did not brake properly when entering the station, hitting the buffers at the platform.
Dozens of emergency personnel were sent to the station, with most of the injured being treated on the platform.
Emergency services said as well as the seriously wounded person, who does not have life-threatening injuries, 19 people were moderately hurt.
They are being treated in hospital. Among them is the driver, who is said to be in a state of shock.
The remainder were lightly injured.