The rescuers did not find anyone trapped in the debris overnight, but a police officer said the clearing operation was continuing Wednesday morning.
A half-dozen vehicles, including a bus, fell with the broken section of concrete, about 100 feet (30 meters) long, in Kolkata's Majerhat neighborhood.
The officer in the police control room said 24 injured people were taken to hospitals. At least one person died, according to an official at the city's Seth Sukhlal Karnani Memorial Hospital who spoke on condition of anonymity because he wasn't authorized to speak publicly.
The nearly 50-year-old bridge ran over the Majerhat railroad station but no train was running at the time, the Press Trust of India news agency reported.
West Bengal Chief Minister Mamata Banerjee told reporters that several transportation workers may have been in a small office under the overpass when the collapse occurred.
It was the second major road collapse in Kolkata in recent years. In 2016, a section of an unfinished overpass collapsed, killing 26 people. An official report later blamed that collapse on bad design and poor-quality materials.