The arrests came after claims by the group it broke into Apple Inc servers and launched attacks last year that shut down sites of MasterCard Inc. and Visa Inc.
Arrests were made in California, Florida and New Jersey, a second law enforcement source said.
Neither source wanted to be identified as charges had not been unsealed.
The arrests followed raids on six locations in New York, including one in Brooklyn and five others on Long Island. They were searched for computers and computer-related accessories, the FBI said.
The equipment was suspected of being used by members of the grass-roots organization inspired by WikiLeaks and its founder Julian Assange.
No arrests were made in New York.
FBI officials in California and Florida said searches were underway but declined to confirm any arrests.
A spokesman for the FBI in New Jersey said one arrest was made there but declined to say where or on what charges.
Court papers for the sweep were expected to be unsealed later on Tuesday.
Anonymous, which law enforcement authorities believe is mostly made up of hackers believed to be in their teens and early 20s, also has released scores of private e-mails and other data from an Arizona police website.
The group teamed up with the Lulz Security group of hackers in June. LulzSec has breached websites of Sony Corp, the CIA and a British police unit.
Experts say the FBI raids should have been expected as the group’s actions have become more daring.
“I don’t think anybody should be surprised,” said Josh Shaul, chief technical officer of Application Security, Inc., which helps companies protect their data. “They played with fire and they got burned.”
(Reporting by Basil Katz in New York, Pascal Fletcher in Miami, Dan Levine in San Francisco and Diane Bartz and Jeremy Pelofsky in Washington)