"They are still pulling out bodies from the rubble, I could hear the screams," a worker with one of the firms involved in the construction of the bridge, who declined to be named, told Reuters news agency.
Le Viet Hung, the deputy head of the Can Tho police, said rescue teams were digging through the rubble in search of survivors.
He said: "It was total chaos. It sounded like a huge explosion.
"It's the biggest accident I've ever seen."
Images broadcast on Vietnamese television showed mounds of twisted steel and cables shrouded in dust and smoke.
Dozens of workers in yellow helmets worked to aid colleagues trapped in the wreckage with some carrying bloody victims on stretchers.
The Japanese-funded bridge was being built across a branch of the Mekong river in the southern city of Can Thothat and was part of a heavily traveled route linking the Mekong Delta and Ho Chi Minh City.
Construction on the 2.75km, four-lane bridge started in 2004 and was expected to be finished next year.
It was to be the largest suspension bridge in Vietnam and intended to greatly speed up the trip across the river, which thousands of people currently make daily by ferry.