The bridge over a river in Shaanxi province's Shangluo buckled at around 8:40 pm Friday (1240 GMT) "due to a sudden downpour and flash floods", state news agency Xinhua said, citing the provincial public relations department.
State broadcaster CCTV said nearly 20 vehicles and more than 30 people remained missing after the highway bridge collapsed into the river below.
All 11 confirmed victims were found inside five vehicles that had so far been recovered from the water, the broadcaster said.
Images on state TV showed a partially submerged section of the bridge with the river rushing over it.
One witness told local media that he had approached the bridge but that other drivers started "yelling at me to brake and stop the car."
"A truck in front of me didn't stop" and fell into the water, the witness, surnamed Meng, said.
Chinese President Xi Jinping has urged "all-out efforts" to find those still missing, CCTV said.
Large portions of northern and central China have been battered since Tuesday by rains that have caused flooding and significant damage.
On Friday, state media reported at least five people dead and eight missing after the rains sparked flooding and mudslides in Shaanxi's Baoji city.
State television broadcast images of neighborhoods completely flooded by muddy water, with excavators and residents attempting to clear the damage.
Extreme weather
The semi-desert province of Gansu, which neighbours Shaanxi, and Henan in central China were also hit by heavy rains this week.
In Henan's Nanyang city, the equivalent of a year's worth of rain fell at the start of the week, according to CCTV.
And in southwestern Sichuan province, two people were reported killed and seven others missing Friday after heavy rain triggered landslides, Xinhua said.
China is enduring a summer of extreme weather, with heavy rains across the east and south coming as much of the north has sweltered in successive heat waves.
Climate change, which scientists say is exacerbated by greenhouse gas emissions, is making these types of extreme weather phenomena more frequent and more intense.
In May, a highway in southern China collapsed after days of rain, leaving 48 dead.
Earlier this month, a tornado passed through a town in eastern China killing one, injuring 79 and causing significant damage.
