Laura Brown, a Federal Aviation Administration spokeswoman, said Flight 1549 had just taken off from LaGuardia Airport en route to Charlotte, North Carolina, when the crash occurred.
The pilot radioed flight controllers that he had hit birds a few miles (kilometres) from the airport, law enforcement sources told the Reuters news agency.
A passenger told Reuters that a few minutes after the plane took off he heard what sounded like and explosion.
"The engine blew. There was fire everywhere and it smelled like gas," Jeff Kolodjay, from Norwalk, Connecticut, told Reuters on a midtown Manhattan quay.
He said the pilot announced that the plane was going down and told passengers to brace for the impact.
"People were bleeding all over. We hit the water pretty hard. It was scary."
The plane initially sank up to its windows, and passengers were taken off the craft into frigid water on one of the coldest days of the year, with temperatures around minus 6.7 degrees Celsius.
Rescuers in Coast Guard vessels and ferry boats opened the door and pulled passengers in yellow life vests from the aircraft.