Bystanders screamed in horror when an eight-year-old boy was pushed in front of an oncoming train , killing him instantly.
A 40-year-old Eritrean man also pushed the boy's mother from the platform but she was able to roll to safety.
Commuters "collapsed" screaming and crying on the platform, one witness said.
A witness told Hessenschau that several children were on the platform when the boy was killed.
The witness, who was on the train, said: "People collapsed howling."
Another witness said the station was "full of children" at the time, and the train conductor was screaming.
The suspect fled the scene in the German city of Frankfurt but was followed by passers-by and later arrested outside the station, reports Der Spiegel.
Police have not found any link between the man, who lived in Switzerland, and the mother and son.
A police spokeswoman said the motive was unclear at this stage of the investigation.
Isabell Neumann told reporters: "According to witness reports, a 40-year-old man pushed the boy and his mother onto the track just as the ICE (high-speed train) was arriving.
"The mother, thank God, was able to save herself.
"Unfortunately, the eight-year-old boy was run over by the ICE. He suffered fatal injuries.
"The man concerned... fled the station after the crime. Passers-by took up the chase and the man was detained near the station."
The man is expected to appear in court today.
The boy's mother was taken to hospital and has also been questioned by police.
Frankfurt police said on Twitter the suspected perpetrator was an Eritrean citizen.
Several platforms at Frankfurt station, a major rail hub in Germany, were closed after the incident.
The police spokeswoman said the man tried to push a third person onto the track but the woman managed to defend herself.
Interior Minister Horst Seehofer strongly condemned the "horrific act" and warned against jumping to any conclusions as police were still investigating.
Seehofer said he would cut short his holidays to discuss the security situation with senior officials on Tuesday and inform the public afterwards.
