Large parts of northern and central China have been battered in recent days by rains that have caused flooding and significant damage.
The bridge in the northwestern Shaanxi province buckled "due to a sudden downpour and flash floods" Friday night, according to state news agency Xinhua.
All 12 victims in the city of Shangluo were found inside five vehicles that were recovered from the river below the bridge, Xinhua said.
At least 31 people remained missing and initial investigations indicated that 17 cars and eight trucks had fallen into the river, it added.
Images on state television 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 rescue and relief efforts" to find those still missing, Xinhua said.
In the southwestern province of Sichuan, more than 30 people were reported missing on Saturday after a violent thunderstorm caused flash flooding in the town of Ya'an, according to state broadcaster CCTV.
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 neighbourhoods 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, CCTV said.
And in 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 heatwaves.
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.
This month, a tornado passed through a town in eastern China killing one, injuring 79 and causing major damage.
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