The accident took place in the Barcelos province, some 400 km (248 miles) from the state capital, Manaus.
The passengers on board the plane were Brazilian tourists on their way to fish, reports said.
“I deeply regret the death of the 12 passengers and two crew members who were victims of the plane crash in Barcelos on Saturday,” said Wilson Lima, Governor of Amazonas state on X, formerly known as Twitter.
“Our teams have been working from the outset to provide the necessary support. My sympathy and prayers go out to their families and friends.”
The Manaus Aerotaxi airline issued a statement confirming that there had been an accident and that it was investigating but offering no details about deaths or injuries.
“We count on respect for the privacy of those involved at this difficult time and will be available to provide all necessary information and updates as the investigation progresses,” the statement said.
The Brazilian Air Force (FAB) said in a statement that investigators from the Accident Investigation and Prevention Center (CENIPA) had been called in to begin an investigation into the reasons for the crash of the small aircraft, an Embraer Bandeirante with the registration PT-SOG.
In an interview with O Globo newspaper, Governor Lima said that the bodies had already been removed and taken to Manaus for formal identification.