The Emirates flight was preparing to take off late Friday when a "verbal threat" was made to staff, London's Metropolitan Police Service said.
"Police were alerted and armed officers boarded the plane," a police statement said.
"Three men aged 58, 48 and 36 were arrested and are now in police custody. They have been arrested on suspicion of making a bomb threat."
Police were searching the aircraft but media reported no harmful substances were believed to have been found on the plane, which had 331 passengers on board.
Sky News television reported that the men arrested were English and appeared to be drunk.
It broadcast a grainy photograph purportedly taken inside the aircraft, showing police in black overalls, and a passenger said officers brandishing guns in body armour burst onto the plane and hauled the suspects away.
The alert came amid heightened security at airports around the world following an alleged attempt by a young Nigerian to bomb a plane landing in Detroit on Christmas Day by concealing explosives in his underwear.
Passenger Cameron McLean, who Sky said supplied them with the photograph, told the broadcaster: "Some special police just came on the plane and arrested these two guys a few rows in front of me.
"The police just swarmed the guy and then rushed him out. I think he was a white male," he said.
The passenger added there were about five armed officers who were wearing helmets, body armour and carrying what appeared to be automatic weapons.
Police said they were alerted after the threat was made at around 9:15pm (2115 GMT) on Friday.
They said passengers had been removed from the plane and the aircraft was being searched. The airport -- one of the world's busiest air hubs -- remained open.
A spokesman for airport operator BAA said the incident had only affected the Dubai-bound plane.
Emirates said officers boarded the plane after "remarks" made as Flight EK004 was preparing to depart.
"The safety and security of all our passengers is paramount," the airline added.
The security scare came after Umar Farouk Abdulmutallab, 23, allegedly tried to detonate a device stitched into his underwear on a flight from Amsterdam as it landed in the United States on December 25.
In a court in Detroit on Friday, he pleaded not guilty to six charges related to the incident, which has led to security being stepped at airports worldwide.
Full-body scanners are to be introduced at Britain's airports and Heathrow will be the first to receive the devices before the end of the month, Home Secretary Alan Johnson has said.
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