The news comes after a former instructor at the school, also an American, was extradited to the US on similar charges, they said.
The kindergarten teacher was seized by Chinese police last month after seven families filed formal accusations against him, alleging sexual abuse and rape of students of both sexes, several parents said.
"As parents we are devastated," said the mother of one pupil, who requested anonymity to protect her child's privacy.
"The investigation is being carried out by the Chinese police and is ongoing. The teacher has been in administrative detention since his arrest," the school added.
The mother said that her child started behaving oddly soon after they moved to the country.
"My daughter was having nervous breakdowns, she was scratching herself on her face and thighs," she said.
"As we had just arrived in China I figured it was exhaustion from moving countries, I didn't worry about it," she said, adding that only later did she link the unusual behaviour to abuse.
Another mother said she suspected her daughter had been abused over a period of months, and that cases of abuse of other children went back as far as five years.
"We are living a nightmare," she said.
The second teacher, a friend of the first, was "extradited by Chinese authorities to the United States in December 2012 following an investigation into sexual touching and violence against minors", the school said in an email.
He left the French school in 2011 and its management said his alleged actions took place during individual classes at a private home, when he was no longer on its staff.
One parent expressed frustration, saying: "The French school wants us to believe that there is absolutely no link between these two incidents, except that the two people, while they were working together, were friends."
The French school in Shanghai is a private institution contracted with the Agency for French Teaching Abroad, a government body.
