Reports say no target had been chosen and no plane tickets purchased by the time the alleged plot was foiled.
Officials say there was never any risk to the public. It is not clear what has happened to the would-be bomber.
Peter King, chairman of the Homeland Security Committee of the US House of Representatives, said counter-terrorism officials had told him: "We don't have to worry about him any more."
The officials revealed that the would-be bomber was alive, but would not say whether he was in foreign custody, Mr King added.
US Secretary of State Hillary Clinton said the foiled attack was proof of the continuing need for vigilance around the world.
"These terrorists keep trying. They keep trying to devise more and more perverse and terrible ways to kill innocent people," she said.
US officials said the device had been seized in an unspecified Middle Eastern country outside Yemen within the last 10 days.
"As a result of close co-operation with our security and intelligence partners overseas, an improvised explosive device (IED) designed to carry out a terrorist attack has been seized abroad," the FBI said.
AnalysisIn spite of recent successes against al-Qaeda in the Arabian Peninsula, Yemen continues to be the focus of US counter-terrorism operations.
Targeted killings carried out by unmanned aircraft, or drones, have become a key component of the CIA's campaign against senior al-Qaeda figures. On Sunday, Fahd al-Quso, wanted by the FBI for his role in the bombing of the USS Cole in 2000, was killed by a missile as he stepped out of a vehicle. It's not clear whether his death was part of the same operation that uncovered the latest plane bomb plot against the US.
The man believed to be responsible for designing the device that would have been used is also said to be hiding in Yemen. Ibrahim al-Asiri, 30, is a Saudi national who helped mastermind the so-called "underwear bomb" plot in 2009 and the 2010 attempt to blow up two cargo planes bound for the US. The FBI says the device it is currently examining is similar but more sophisticated than the ones used in those previous attacks.
The BBC's Mark Mardell in Washington says the plot, disrupted as a result of US co-operation with other unnamed intelligence agencies, appears to have been caught at a relatively early stage - after the making of the bomb, but before the public was put at risk.
"What this incident makes clear is that this country has to continue to remain vigilant against those that would seek to attack this country. And we will do everything necessary to keep America safe," Defence Secretary Leon Panetta told reporters on Monday.
Although other agencies were involved, senior Yemeni officials say the government in Sanaa there has no information on this particular plot, according to Reuters news agency.
Officials said it appeared that AQAP leaders in Yemen had instructed a suicide bomber to board any flight of his choosing to the US with the bomb under his clothes, but that he had been stopped before reaching an airport.
It is not clear who built the alleged device, but officials said it shared some features with the bomb sewn into the underwear of would-be suicide bomber Umar Farouk Abdulmutallab.
The Nigerian was arrested when his device failed to explode fully while on a plane bound for Detroit on Christmas Day 2009.
'Bomb plot': Unanswered Questions
- Unclear who the would-be bomber is or whether he/she is in custody
- Country where alleged device was seized as yet unspecified
- No information on how the alleged plot was intercepted
- Exact composition of alleged device unclear, although said to contain no metal parts and designed to escape detection by magnetometers at airport security
It is not even clear if it would have been found by the body scanners that have been installed in some US airports after that attempted attack three years ago.
Abdulmutallab's "underwear bomb" was not detected during security checks at airports in Lagos, Nigeria, and Amsterdam before he boarded Northwest Airlines Flight 253 for Detroit.
On the flight, the bomb did not detonate fully and passengers had to put out the fire. He has been sentenced to life in prison.
In a previous incident that year, a man also equipped with a bomb in his underwear tried to attack Prince Mohammed bin Nayef, a senior Saudi Arabian counter-terrorism official. The bomber killed himself in the attack, but the prince survived.
In a statement, the Department of Homeland Security said air security would continue to incorporate threat and vulnerability analysis, pre-screening and screening of passengers, as well as random searches at airports, air marshals and other unspecified security measures.
News of the operation emerged shortly after the US marked the first anniversary of the death of al-Qaeda leader Osama Bin Laden.
It also comes one day after Fahd al-Quso, an al-Qaeda leader in Yemen, was killed by a US drone strike.
The US had offered a $5m (£3.1m) reward for information leading to Quso's capture or death.
The Yemeni government has stepped up its battle against AQAP since Ali Abdullah Saleh stepped down as president in November.
However, the group and its allies still control large parts of the country.