The alert identifies a Yemeni national - and more than 10 associates - the FBI believes could be plotting an attack in the US or Yemen.
The man is named as Fawaz Yahya al-Rabeei - who is believed to have been born to Yemeni parents in Saudi Arabia in 1979.
The US has been on a high state of alert since the terror attacks on New York City and Washington DC.
Following the latest warning, a Yemeni security official said his government had taken all the necessary steps to prevent a possible attack.
And work was continuing normally at the White House in Washington and at the US consulate in the Yemeni capital, Sanaa.
Alert message
"A planned attack may occur in the United States or against US interests in the country of Yemen on or about 12 February 2002," the FBI alert said.
US officials said the information leading to the alert came from interviews carried out in Afghanistan and at Guantanamo Bay in Cuba, where a number of al-Qaeda and Taleban suspects are being held.
The alert said most of the suspects came from Saudi Arabia and Yemen, with possibly one of Tunisian origin.
"We had credible information, we had a specific name," White House spokesman Ari Fleischer said.
The FBI said it was not known whether Fawaz Yahya al-Rabeei was in the US.
The alert listed a dozen aliases for him, including "Furqan".
Police forces across America have been asked to stop and detain any of the individuals named in the alert.
The FBI said all of them "should be considered extremely dangerous".
Fourth alert
This is the fourth general alert to be issued by the FBI and the newly-established Homeland Security Council.
Mr Fleischer said the alert was meant as a preventive measure.
"It's exactly this type of action that helps disrupt or prevent terrorist attacks, which is why the FBI does it - and properly so," Mr Fleicher said.
He said President George W Bush had not altered his public schedule, and Vice President Dick Cheney, who has gone to secure locations during times of high alert, was working at the White House.
The most recent alert preceding the latest warning was issued in early December to cover the Christmas holiday period.
It was then extended to include the Salt Lake City Winter Olympics, and is due to expire on 11 March.
Other warnings to specific locations and industries - including nuclear power plants - have also been issued.
Yemen was the site of an attack in October 2000 when the American warship USS Cole was bombed in the southern port of Aden. Investigations have been continuing into the attack which killed 17 US servicemen.