Human remains have been found at the scene and there are no signs of survivors, according to the Federal Bureau of Investigation.
Atlas Air Flight 3591 was traveling from Miami to Houston when it crashed into Trinity Bay, near Anahuac, Texas.
Chambers County Sheriff Brian Hawthorne said eyewitnesses reported the plane crashed nose-first into the bay.
"I feel like it's probably a crash that nobody would be capable of surviving," said Hawthorne said.
The plane was operating for Amazon, Atlas Air said Saturday. Atlas Air is one of the cargo airlines that Amazon contracted to operate the Amazon-branded fleet, called Amazon Air, along with Air Transport Services Group. Each operates 20 Amazon-branded planes for the air freight service, which was previously called Prime Air.
Video taken at the crash site by local news outlets showed debris in the bay, including a piece of material that appeared to feature a part of Amazon's logo. Hawthrorne said the crash site is in a muddy and marshy area of the bay and that law enforcement spotted items including bed sheets, women's clothing and cardboard boxes in the bay.
The flight lost radar and radio contact about 30 miles southeast of its destination, Houston's George Bush Intercontinental Airport, said the FAA.
"FAA investigators are on their way to the accident site, and the National Transportation Safety Board has been notified," said FAA spokesman Lynn Lunsford in a statement. "The NTSB will be in charge of the investigation."
The NTSB said it was sending a "go team" to the crash site on Saturday evening from Washington D.C.
Atlas Air confirmed that three people were on board the aircraft.
"Those people and their family members are our top priority at this time," the company said in a statement. "Atlas Air is cooperating fully with the FAA and NTSB. We will update as additional information becomes available."
Boeing, which manufactured the plane, said it in a statement that it "is deeply saddened to learn of the accident.
"We are concerned about the safety of the three people reported to be on board the airplane," said the statement.
Boeing added that it would provide technical assistance to the NTSB's investigation.
The Boeing 767 was powered by GE CF6-80C2 engines, one of General Electric's most popular aircraft engines. The company said in a statement that it was aware of the accident and it has a team in place to "provide all the necessary support required."
"Our thoughts and prayers are with the flight crew, their families and friends along with the entire team at Atlas Air during this terrible tragedy," Dave Clark, Amazon's senior vice president of worldwide operations. "We appreciate the first responders who worked urgently to provide support."
-CNBC's Phil LeBeau contributed to this report.