Photos taken after the accident showed a Boeing 747 cargo aircraft with AirACT livery partially submerged in water near the airport's sea wall with an escape slide deployed and the nose and tail sections separated.
The four crew members on board the plane were rescued, the Hong Kong airport said in a statement.
Two people inside a ground vehicle near the runway that was suspected to have been struck by the aircraft had died, the South China Morning Post reported, citing police.
Police did not immediately respond to a request for comment.
The northern runway at the world's busiest cargo airport is closed after the incident, Hong Kong International Airport said, adding the south and central runways would continue to operate.
The accident happened about 3.50am (local time).
Emirates said in a statement that flight EK9788 sustained damage on landing in Hong Kong on Monday and was a Boeing 747 cargo aircraft wet-leased from and operated by ACT Airlines.
"Crew are confirmed to be safe and there was no cargo onboard," Emirates said.
ACT Airlines is a Turkish carrier that provides extra cargo capacity to major airlines. It did not respond immediately to a request for comment outside normal business hours.
Flight tracking service FlightRadar24 said the aircraft involved in the accident was 32 years old and had served as a passenger plane before being converted into a freighter.
