CNA quoted a government spokesman as saying the plane crashed after hitting an elevated bridge.
Footage of the plane apparently filmed from inside passing cars showed it banking sharply and clipping the bridge before crashing into the river.
Taiwan's aviation authority later said at least two people had been killed.
Television images showed rescuers standing on large sections of broken wreckage trying to pull passengers out of the plane with ropes.
Those that were rescued were helped into dinghies and taken to shore.
In July last year 48 people died when a TransAsia Airways plane crashed amid stormy weather in Taiwan's Penghu archipelago.