A knife-wielding man set fire to a train in north-eastern Switzerland, along the border with Liechtenstein.
Six victims are in hospital with stab wounds and burns, police said.
The Israeli Foreign Ministry said that there were no Israelis among the casualties.
The suspected attacker, described as a Swiss citizen aged 27, was also injured and taken to hospital after the incident near Salez in St Gallen Canton. He had ignited a flammable liquid before stabbing his victims.
Among those who were hurt was a six-year-old child. Also hurt were a girl and a boy, both aged 17, two women aged 34 and 43, and a man aged 50. Some of the injured are said to be in a serious condition.
"We can neither exclude nor affirm that this was a terrorist act," Saint Gallen regional police spokesman Bruno Metzger told the local St.Galler Tagblatt daily.
Police spokesman Hanspeter Kruesi told AFP the suspected attacker was a Swiss national, and not of immigrant background. He did not comment on whether the attacker's religious affiliation was
known to police.
One woman and the attacker were "very seriously injured", Kruesi told AFP, adding that both their lives were in danger. He said no one had overpowered the attacker, but that he had been hurt in the fire.
Kruesi denied reports that the man had targeted one specific woman on the train, dousing her with the flammable liquid. "That is not correct. This was not directed concretely at one person," he said, adding that it remained unclear whether the attacker knew any of his victims.
St Gallen Police added: "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."
Three rescue helicopters were reportedly at the scene and a major police operation was under way.
The attack occurred around 2:20 PM local time as the train approached Salez station, between the towns of Buchs and Sennwald. There were several dozen passengers on board at the time of the attack.
It is not yet known if the attacker is a Muslim.