St Gallen Police confirmed the attack today.
The attack happened on the line between Buchs and Sennwald at around 2.20pm, before the train reached Salez station.
A man on the train used flammable liquids to attack men, women and children in north west Switzerland.
The suspected attacker was taken to hospital after the incident near Salez in St Gallen Canton, Swiss media has said.
St. Gallen cantonal polices spokesman Bruno Metzger said: “Among the injured is at least one child.”
Police later said three 17-year-olds were among the injured, as well as a 50-year-old man, as well as the six-year-old child.
Two other victims were 34 and 43.
Several dozen passengers were on board at the time of the attack.
Police, ambulances and helicopters remain on scene in Switzerland but the attacker is in hospital
A police statement said the assailant was a 27-year-old Swiss citizen and that he was also injured in the incident.
It was not clear whether the man was under arrest and the statement revealed no possible motive for the attack, but did say a criminal inquiry was under way.
The statement said: ”According to current information a 27-year-old Swiss man poured out a flammable liquid. He was also armed with at least one knife. The liquid caught fire.”
Swiss police later said they have not ruled out the motive being a “crime of passions”.
A police spokesman told welt.de: “A terrorism background still seems very, very far-fetched.”
The attack took place on a train right before it reached the station in Switzerland
It is the first attack of its kind in Switzerland in recent memory.
There have been a string of assaults on the public in neighbouring France and Germany, as well as Belgium, over the past 18 months, most of which were claimed by the Islamic State militant group and killed more than 250 people.
Armed police have been called to the scene, as well as ambulances and helicopters
Passengers are reported to be “seriously injured”.
Emergency services have surrounded the scene, including firefighters, three rescue helicopters, two emergency physicians, three ambulances and experts from the railway companies.