"Three people have been arrested at Heathrow this evening. They are currently in police custody. The airport remains open,'' a statement from London's Metropolitan Police Service said.
Friday evening's 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.
Sky News television said police intervened after verbal threats were made and that the men arrested were English and appeared to be drunk.
The broadcaster showed a photograph purportedly of officers in black overalls inside the aircraft, taken by a passenger on the flight.
"Some special police just came on the plane and arrested these two guys a few rows in front of me,'' Mr McLean said.
"The police just swarmed the guy and then rushed him out. I think he was a white male. There was another one as well, I didn't see him,'' he said.
One of the men was taken off in handcuffs, Mr McLean said.
The passenger added there were about five armed officers who were wearing helmets, body armour and carrying what appeared to be automatic weapons.
A spokesman for airport operator BAA confirmed a "security incident'' on the plane but said it only affected the Dubai-bound Emirates plane.
The alert 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 Detroit on Christmas Day.
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 - one of the world's busiest air hubs - will be the first to receive the devices before the end of the month, Home Secretary Alan Johnson has said.