Hamza, 47, was arrested under the Terrorism Act 2000 "under suspicion of being involved in the commission, preparation or instigation of acts of terrorism", the Metropolitan Police said in a statement.
"He has been taken into custody to a central London police station where officers from the anti-terrorist branch will interview him," they said, adding that the arrest had been made as part of a "domestic investigation".
The Egyptian-born cleric, who gained notoriety for his fiery sermons at north London's Finsbury Park mosque, has been behind bars at the high-security Belmarsh prison in south-east London since May.
He was arrested at that time on suspicion of carrying out a key role in Osama bin Laden's al Qaeda network and detained at Belmarsh.
The hook-handed cleric faces extradition to the United States on 11 terrorism-related charges, notably over a hostage-taking in Yemen in 1998 and an alleged al Qaeda training camp operating in Oregon in 1999-2000.