The 22-year-old woman, named locally as Hanan al Samawi, was traced through a phone number left with a cargo company. Ali Abdullah Saleh, Yemen's president, said the information that identified her was provided by the US and the United Arab Emirates.
She was arrested at a house in a poor area in the west of Sana'a, where she is studying medicine at the university. Her mother was also arrested, but is not a prime suspect according to her lawyer.
The bomb intercepted in Britain on its way to America was designed to explode in mid-air and may have been targeted at the UK.
David Cameron said he believed the device was constructed to detonate while the aircraft was in flight.
He said a plot to blow it up over British soil could not be ruled out.
The Prime Minister's dramatic intervention came as the investigation into the plot was centring on one of al-Qaeda's most senior commanders.
US and British security officials believe Anwar al-Awlaki, the American-born figurehead of al-Qaeda in the Arabian Peninsula (AQAP) was behind the foiled attack in which two ink cartridge bombs, posted in Yemen, were intercepted in Britain and Dubai on the way to America.
Al-Awlaki, who is in hiding in Yemen, is regarded by the CIA and MI6 as the driving force behind the transformation of AQAP from a regional group into an international terrorist organisation.
Fears of more plots emerged after investigators in Sana'a, the Yemeni capital, said they were examining 24 other suspect packages.
Mr Cameron's comments, in a televised address from Chequers shortly after 6pm, were the first suggestions that Britain could have been in the line of fire.
He said there was "no early evidence" that Britain was targeted, but added: "We believe that the device was designed to go off on the aeroplane. There is no early evidence that it was designed to go off over British soil, but, of course, we cannot rule that out."
Had the planes been brought down over populated areas, hundreds could have been killed.
In Sana'a, authorities were also questioning cargo workers at the airport and employees of shipping companies contracted to work with the freight companies FedEx and UPS.
While the devices were addressed to synagogues in Chicago, Theresa May, the Home Secretary, was the first to announce that the target for the bombs could have been the planes.
She also said the Government had launched a review of Britain's air cargo security and disclosed that all unaccompanied freight from Yemen had been stopped.
Further suspicion fell on the involvement of AQAP when Janet Napolitano, the US Homeland Security Secretary, claimed that the plot had all the hallmarks of an al-Qaeda "spectacular".
It was well orchestrated, it targeted airlines and it was designed to cause global panic and chaos.
The devices were believed to be similar to those developed by Ibrahim Hassan al Asiri, a Saudi jihadist who is thought to have designed a bomb smuggled on to a US-bound Christmas Day flight last year by Umar Farouk Abdulmutallab, the so-called Underpants Bomber.
Asiri is also believed to have constructed a bomb that was hidden in a body cavity of his brother who blew himself up while trying to kill Prince Mohammed bin Nayef, Saudi Arabia's top counter-terrorism official, who survived the attack.
Speaking after a meeting of Cobra, the Government's emergency planning committee, Mrs May said: "I can confirm that the device was viable and could have exploded.
"The target may have been an aircraft and had it detonated the aircraft could have been brought down.
"But we do not believe that the perpetrators of the attack would have known the location of the device when they planned for it to explode.
"At this stage, we have no information to indicate another attack is imminent. The threat level is already at severe, meaning that a terrorist attack in this country is highly likely. We do not plan to change that threat level at this stage."
The Prime Minister said that he had spoken by telephone to President Saleh and the Saudi ruler, King Abdullah, as well as to Barack Obama, the US President.
Mr Cameron said: "We have to do more to cut out the cancer of al-Qaeda in Yemen and the Saudi peninsula."
The announcement brought to a head 24 hours of confusion during which Leicestershire police, at first, failed to identify explosives in a suspect package. After a device was found in Dubai, police carried out further checks and found the bomb.
Security sources told The Sunday Telegraph that an airborne attack was thought to be the terrorists' most probable tactic.
"We think it is probably a more likely scenario than others, but it's pretty convoluted. We have not yet done all the full tests," said the source.
Mobile phones can be used as the trigger to detonate a bomb, by either using the handset's internal clock as a timer or setting it to detonate when the phone receives a call or a text message.
The international terror alert was launched late on Thursday when MI6 received information from their counterparts in the Saudi Arabian intelligence services warning of a plot.
Following the tip-off, security staff discovered suspicious packages on board planes at cargo hubs at East Midlands Airport and Dubai.
The packages were addressed to synagogues in Chicago, and were on Chicago-bound cargo flights.
After examining the Dubai device, local police said: "The parcel was prepared in a professional manner where a closed electrical circuit was connected to a mobile phone SIM card hidden inside the printer. This tactic carries the hallmarks of methods used previously by terrorist organisations such as al-Qaeda."
The bomb also contained lead azide, an explosive compound that can be used in detonators, together with the powerful explosive pentaerythritol tetranitrate (PETN).
This is the same chemical used by Abdulmutallab in the plot to blow up a plane over Detroit on Christmas Day last year.
Following the latest discoveries, UPS jets in Philadelphia and Newark, New Jersey, were moved away from terminal buildings and two fighter jets escorted an airliner travelling into New York from Dubai.
As speculation grew on both sides of the Atlantic, President Obama broke the news that the discovery of the two devices meant the West was once again dealing with "a credible terrorist threat".
The terror alert followed calls this week from airline bosses for existing security procedures such as shoe and laptop checks to be scrapped.
The plot resembles the Lockerbie bombing of Pan Am Flight 103, which also featured concealed explosives within an electronic device, a radio cassette player.
Last month, Jonathan Evans, the director general of MI5, warned in a speech that his organisation had seen a "surge" in Yemen-related case work over the past 12 months.