Dramatic video footage emerged showing the TransAsia Airways plane clipping a bridge as it came down shortly after take-off from a Taipei airport.
The plane, carrying 58 people, broke up as it plunged into Taipei's Keelung River. The fuselage was later salvaged by crane.
There were 15 survivors pulled from the wreckage but 12 people remain missing.
Television footage showed some passengers wading clear of the sunken wreckage and a toddler being pulled out alive by rescuers.
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 ATR-72 turbo-prop plane had just taken off from Taipei Songshan Airport and was heading to the Kinmen islands, just off the coast of the south-eastern Chinese city of Xiamen.
It is the second TransAsia ATR-72 to crash in seven months, following an accident last July which killed 48 people and injured 15.
The final communication from the pilots to air traffic control was "Mayday, mayday, engine flame out", according to a recording played on local media. The recording was not immediately verified by aviation officials.
Yet again, we are looking at shocking pictures of a plane crash. You'd be forgiven for thinking that flying is getting more dangerous, but it's not. In fact, when you look at the number of crashes and fatalities compared to the huge number of people flying today, we are in a golden era of aircraft safety.
According to safety analysts Ascend, 2014 was narrowly the safest year ever, with one fatal accident per 2.38 million flights, compared to every 1.91 million flights in 2013. That does not include the loss of the Malaysian airliner over Ukraine, where 298 people died, which they count as a war loss rather than an accident.
Nearly a thousand people died in 2014, which is 700 more than the year before. Horrible numbers but compare that to the worst year, 1972, when 2,370 passengers were killed. There was far less flying then, maybe a quarter of what there is today.
Nothing is ever without risk, but the chances of dying in an aircraft "accident" are lower than ever.
Flight controllers lost contact with the plane at 10:55 local time (02:55 GMT).
Footage of the plane filmed from inside passing cars showed it banking sharply, hitting a taxi and clipping the bridge before crashing into the river.
"I saw a taxi, probably just metres ahead of me, being hit by one wing of the plane," an eyewitness told local media.
"The plane was huge and really close to me. I'm still trembling."
TV footage showed rescuers standing on the tail section of the broken wreckage trying to pull passengers out of the plane with ropes.
One Taiwanese father told reporters he managed to rescue his wife before noticing his two-year-old son was still trapped underwater. The boy was later rescued but is believed to be in critical condition.
The majority of the plane, including the front section of the fuselage and the wings, was submerged after it plunged into the Keelung River.
Jaime Molloy, an English teacher who has lived in Taipei for three-and-a-half years and works near the scene of the crash, told the BBC: "The most disturbing scenes I saw were the debris, which included carry-on luggage and personal effects, as well as parts of the plane."
TransAsia said it had contacted relatives of all the 22 Taiwanese passengers on board and was attempting to reach relatives of the Chinese nationals.
Among the 15 injured, there were 11 from Taiwan, three from China and one member of the crew. The airline said that one injured passenger had already been discharged from hospital.
The BBC's Cindy Sui in Taipei says the Chinese tourists could have been on their way home as many people come to Taiwan through Kinmen island.
TransAsia chief Chen Xinde offered a "deep apology" in a televised news conference, but said his planes had been "under thorough scrutiny" since mid-2014.
"Both our planes and our flight safety system are following strict regulations, so we also want to know what caused the new plane model to crash, but I don't want to speculate," he said.
The plane's flight data recorders, also known as black boxes, have been recovered.
A plane carrying mostly Chinese tourists has crashed into a river in Taiwan, killing at least 31 people.