The aircraft experienced a strong shake and as a result, 10 passengers and three cabin crew members were taken to a hospital, the South American carrier said as it investigates the cause.
The flight with 263 passengers and nine cabin crew members landed at Auckland airport as scheduled on Monday afternoon.
One person is in a serious condition while the rest suffered mild-to-moderate injuries, a spokesperson for Hato Hone St John, which treated roughly 50 people at the airport, said.
"The plane, unannounced, just dropped. I mean it dropped unlike anything I've ever experienced on any kind of minor turbulence, and people were thrown out of their seats, hit the top of the roof of the plane, throwing down the aisles," passenger Brian Jokat told the BBC.
The cause of the apparent sudden change in trajectory of LATAM 800 could not be ascertained immediately. Safety experts say most airplane accidents are caused by a cocktail of factors that need to be thoroughly investigated.
"Some of the roof panels were broken from people being thrown up and knocking through the plastic roof panels in the aisle ways. And there was blood coming from several people's heads." Jokat, who was not injured in the incident, said.
He said passengers who were doctors on the plane provided bandages and neck braces for people who were severely injured.
Boeing said it was working to gather more information and will provide any support to the airline.
Boeing shares closed down about 3%, after the latest incident involving one of its aircraft. The U.S. Federal Aviation Administration in January barred the troubled planemaker from expanding production of its best-selling 737 MAX narrowbody planes, following "unacceptable" quality issues.
The head of the FAA, Mike Whitaker, said the agency will work with Australian authorities or the New Zealand authorities to investigate.
"We will certainly follow that closely" given the airplane was manufactured in the U.S., he said.
The U.S. National Safety Board said it did not yet have anything official on the incident.
The eight-year-old Boeing BA.N 787-9 Dreamliner, according to flight tracking website FlightRadar24, was on its way to Santiago via Auckland. LATAM Airlines said a new flight to Chile will depart from Auckland on Tuesday.
In 2008, dozens of people were injured when another wide-body jet, an Airbus 330 operated by Qantas Airways, dropped sharply because of faulty readings from a flight data computer while heading for Perth in Australia.
