Friends and relatives have accused overzealous prosecutors of contributing to the 26-year-old's suicide. He was found hanged in his New York apartment earlier this month.
Swartz was just 14 when he co-developed the RSS feeds that are now the norm for publishing updates online and went on to help launch social news website Reddit.
"As a result of the FBI's infiltration and entrapment tactics, several more of our brethren now face similar disproportionate persecution, the balance of their lives hanging on the severely skewed scales of a broken justice system," Anonymous said in a video posted on YouTube.
The hackers said they had infiltrated several US government computer networks and copied secret data that they could release.
Likening the data to a nuclear weapon, Anonymous said it had "enough fissile material for multiple warheads" it could launch against the Justice Department and agencies that the group says intrude on individual liberties.
The FBI said in a statement that it was investigating the attack.
"We were aware as soon as it happened and are handling it as a criminal investigation," said Richard McFeely, of the bureau's Criminal, Cyber, Response and Services Branch.
The Anonymous operation came just days after US Homeland Security Secretary Janet Napolitano warned of a looming "cyber 9/11" that could especially target critical infrastructure planks such as water, electricity and gas lines.
The loosely affiliated network of hacktivists, has attacked sites around the world, including those of MasterCard and Visa, the US Justice Department as well as the Tunisian and Yemeni governments.
- AAP