Dramatic pictures taken by a motorist and posted on Twitter showed the plane cart wheeling over a motorway close to the airport soon after the turboprop ATR 72-600 aircraft took off.
Television footage showed passengers wearing life jackets wading and swimming clear of the river.
Emergency rescue officials in inflatable boats crowded around the partially submerged fuselage, lying on its side in the river, trying to help those on board.
The civilian aeronautic authority said soon after the crash that two people had been killed. Taiwanese television later reported the death toll had risen to nine.
Other Taiwanese government authorities said the plane was carrying 58 passengers and crew, including 31 tourists from mainland China.
The weather appeared to be clear when the plane took off. Television pictures also showed some damage to a bridge next to the river, with small pieces of the aircraft scattered along the road.
Emergency teams cut open the plane while it was in the water but were unable to reach the passengers trapped in the front section of the fuselage.
As night fell, a crane was used to lift the wreckage on to the bank. The death toll was expected to rise as rescue teams searched the fuselage and the river for the 12 missing passengers.
“At the moment, things don’t look too optimistic,” Wu Jun-hong, a Taipei fire department official coordinating the rescue effort told reporters.
The crash-landing is the latest in a string of mishaps to hit Asian carriers in the past 12 months. An AirAsia jet bound for Singapore crashed soon after taking off from the Indonesian city of Surabaya on Dec. 28, killing all 162 people on board.
Also last year, a Malaysia Airlines jet disappeared and one of its sister planes was downed over Ukraine with a combined loss of 539 lives.
TransAsia is Taiwan’s third-largest carrier. One of its ATR 72-500 planes crashed while trying to land at Penghu Island last year, killing 48 of the 58 passengers and crew on board.
The plane involved in Wednesday’s mishap was among the first of the ATR 72-600s, the latest variant of the turboprop aircraft that TransAsia received in 2014.
They are among an order of eight placed by TransAsia in 2012. The aircraft have 72 seats each. The planes are mainly used to connect Taiwan’s capital, Taipei, to the island’s smaller cities.
The airline also operates Airbus A320 and A330 planes on domestic and international services.
ATR is a joint venture between Airbus and Alenia Aermacchi, a subsidiary of Italy’s Finmeccanica services.