Chinese media report that one of the trains came to a halt after being struck by lightning and was then hit by the second train.
Rescue workers are at the scene, near Shuangyu town in Wenzhou.
It is not known how many people were on the trains at the time, but Xinhua news agency says each carriage can carry 100 people.
Initial reports suggested one bullet train had derailed at about 2030 (1230 GMT) - the D3115 travelling from the provincial capital Hangzhou.
But local television later said the first train had been forced to stop after losing power due to a lightning strike, and was then rear-ended by another train, the D301, causing two of its carriages to fall off an elevated section of track.
TV pictures showed one carriage lying on its side under the bridge, and the other standing on its end leaning up against the bridge. There were reports that four carriages from the other train had also derailed, but it is not known if that led to further casualties.
"D" trains are the first generation of bullet trains in China, with an average speed of just short of 100mph (160km/h).
"The train suddenly shook violently, casting luggage all around," one survivor, Liu Hongtao, was quoted by Xinhua as saying. "Passengers cried for help but no crew responded."
China is spending billions on constructing a high-speed rail network.
Last month China inaugurated its Beijing-Shanghai high-speed rail link. The 300 km/h (190mph) train halves the journey time to under five hours.
But the project has come under fire for its high cost - the Beijing-Shanghai line cost 215bn yuan ($33bn; £21bn). It has also been blighted by power outages and other problems.
China is planning to roll out high-speed lines across the country.
The BBC's Martin Patience in Beijing says there are also fears corruption has compromised safety in the network's construction.