German prosecutors laid murder and attempted murder charges against the 40-year-old, who had on Tuesday also pushed the boy's mother onto the tracks at Frankfurt's main station, and tried but failed to do the same to a 78-year-old woman.
The mother, also 40, was able to roll off the tracks at the last moment to avoid the arriving ICE train that killed her son.
The man, who was arrested shortly after, did not previously know the victims and showed no signs of alcohol or drug use, said Frankfurt public prosecutors spokeswoman Nadja Niesen.
"The crime suggests a psychiatric disorder," she told a press conference.
"In the course of the subsequent investigation, the accused will certainly be psychiatrically examined, to allow an assessment of his criminal culpability."
The horrific crime dominated newspaper front-pages and TV news bulletins, while citizens laid flower wreaths, candles and stuffed toys at the site of the killing.
A memorial service was scheduled at the station at 1630 GMT.
German Interior Minister Horst Seehofer cut short his summer holiday to meet the heads of major security agencies in Berlin Tuesday before giving a press conference.
Frankfurt prosecutors said in a statement that "a 40-year-old man from Switzerland with Eritrean citizenship is accused of having first pushed a 40-year-old woman ... and then her eight-year-old son in front of an approaching ICE express train.
"Subsequently, he tried to push another woman into the track bed but failed.
"While the mother could roll off after the fall and move herself onto a narrow footpath between two tracks, her child was caught by the arriving train and died, on the spot, of his injuries."
The man ran down a platform and across tracks but was followed by passers-by, including an off-duty police officer, and overpowered by police two blocks from the station.
Niesen said the man had not yet spoken about his motive.
He had lived in Switzerland since 2006, was a married father of three, and had told police he had arrived several days ago by train from Basel, Niesen said.
If formally charged, tried and then found guilty, he would face a likely term of life in prison, she said.