The website of the commission, an independent agency of the judicial branch, was taken over early Saturday and replaced with a message warning that when Swartz killed himself two weeks ago "a line was crossed."
The hackers say they've infiltrated several government computer systems and copied secret information that they now threaten to make public.
Family and friends of Swartz, who helped create Reddit and RSS, say he killed himself after he was hounded by federal prosecutors.
U.S. Attorney Carmen Ortiz, in the wake of the suicide, said she believed the case was conducted "reasonably" and "appropriately."
Officials say he helped post millions of court documents for free online and that he illegally downloaded millions of academic articles from an online clearinghouse.
The FBI's Richard McFeely, executive assistant director of the Criminal, Cyber, Response, and Services Branch, said in a statement that "we were aware as soon as it happened and are handling it as a criminal investigation. We are always concerned when someone illegally accesses another person's or government agency's network."
Swartz's supporters believe Ortiz's office was overly aggressive in charging Swartz with 13 felonies for tapping into the computer network at the Massachusetts Institute of Technology to download nearly five million articles from an online clearinghouse for academic journals.
Swartz's lawyer, Elliot Peters, said prosecutors were insisting that any plea deal would involve Swartz pleading guilty to all 13 felony charges against him and serving four to six months in prison.
Ortiz has said her prosecutors did not demand that Swartz plead guilty.Suggest a correction