Three children died at the scene of the accident in Guixi city in Jiangxi province and another eight died later in hospital, said an official from the propaganda office of the city's Communist Party committee. Four children survived, said the official, who like many Chinese bureaucrats gave only his surname, Jiang.
The accident is the latest in a string of deadly crashes in China involving school children.
Police detained the driver for questioning and were investigating the cause of the accident, the official Xinhua News Agency.
Photos on the Shanghai-based Oriental Morning Post's website showed a silver minivan partially submerged in a grassy pond, with one of its three windows on the right side broken.
The minivan belonged to Chunlei kindergarten, which doesn't have a government license to operate, according to an article on the website of state broadcaster China Central Television that didn't cite any sources. The van taking the children to school was travelling too fast and swerved to avoid a vehicle parked on the side of the road, ending up in the pond, CCTV said.
Photos on its website showed pairs of tiny shoes and brightly colored school bags lined up on the ground near the scene and an injured child being treated.
The Hong Kong-based Information Center for Human Rights & Democracy said in a statement that cited no sources that the van was made to carry seven people but was overloaded with 17. The human rights group also said it took 70 minutes for an ambulance to arrive.
Overcrowding on school buses is common in rural China, where the education system is short of funds and children are forced to travel far to get an education because of school closures.
Last year, a nine-seat private school van overloaded with 62 kindergarten children and two adults crashed head-on with a truck in rural western China, killing 19 children and the adults. The accident caused public uproar and Chinese Premier Wen Jiabao pledged more support for school bus safety and said central and local governments would bear the cost of bringing often-shoddy buses up to standard.
Accidents happen frequently in China because of poorly maintained vehicles and reckless driving habits.