The suspect, who US Government sources say was caught in the past few weeks, has not been named.
"I can't tell you when, I can't tell you where, I can't tell you how," said one unnamed official. "But this is a big deal."
The sources said an operation was under way to get the person arrested out of the country where he is currently being held by US forces to a place where he can be interrogated.
Bin Laden voice
Sources told the Reuters news agency that the person who had been captured was neither al-Qaeda leader Osama Bin Laden's right-hand man, Ayman al-Zawahri, nor operational leader Khalid Shaikh Mohammed, nor Bin Laden's son Saad.
Al-Qaeda is blamed for the 11 September 2001 attacks on New York and Washington.
Despite declaring a war on terror following those attacks, the United States has managed to detain only about half of the top 20 or so al-Qaeda members on its "most wanted" list.
Among those held by the US are Abu Zubaydah and Ramzi Binalshibh who are being interrogated at undisclosed locations.
An indication that Bin Laden himself is still alive emerged this week with the release of an audio recording said to have been made by the al-Qaeda leader, praising recent attacks on Western targets.
US officials have said they believe the voice on the tape to be that of Bin Laden.
The FBI has warned that al-Qaeda could be planning "spectacular" new attacks in the United States, possibly targeting national landmarks.