Earl Krugel, 62, was killed in an assault Friday evening at the Federal Correctional Institution, said FBI agent Richard Murray.
Murray wouldn't release further details but said federal authorities had opened a homicide investigation.
Krugel's wife, Lola, said FBI investigators told her an inmate had struck her husband on the head from behind with a cement block.
"Earl never saw it happening," she said. "He was exercising."
He had been at the medium-security prison for three days, according to his sister Linda Krugel, also of Los Angeles.
Earl Krugel, a former dental assistant from Los Angeles, and late JDL leader Irv Rubin were arrested in 2001 and charged with conspiring to bomb the King Fahd Mosque in Culver City and a field office of Republican Rep. Darrell E. Issa, who is Lebanese-American.
Krugel pleaded guilty in 2003 to one count of conspiracy to violate the civil rights of worshippers at the mosque and one count of carrying an explosive device in connection with a conspiracy to impede or injure an office of the United States.
Despite the plea, he was sentenced in September to 20 years in prison. The reasons for the collapse of an initial plea agreement were sealed, despite a lawsuit by news organizations, including The Associated Press, to make the details public.