Law enforcement authorities confirmed the 21-year-old Lindh was attacked but would not disclose a possible motive.
The incident happened Monday night at the medium-security federal prison in Victorville as Lindh was preparing to pray, said his lawyer Tony West.
"Our understanding is that the inmate tackled John and began hitting him while screaming obscenities before running off," West said in a statement. Lindh suffered a bruise on his forehead, the lawyer said.
"John is fine," West said. "He's in very good spirits."
A law enforcement official, speaking on condition of anonymity, said: "It was a minor incident, a prison fight. He got a little scraped up, but he's fine. One guy was picking on him."
The official had no information on Lindh's attacker.
The FBI said Thursday it was investigating.
The investigation started after the San Bernardino County Sun received an anonymous tip early Tuesday.
"Yes, I'd like to inform your newspaper that John Lindh Walker, who is incarcerated in Victorville, was assaulted this night by a white supremacist organization that is imprisoned there. Thank you," the male caller said in a voice message.
Lindh was sentenced in October to 20 years in prison after pleading guilty to supplying services to Afghanistan's Taliban government and carrying explosives in commission of a felony.
He has been at the prison northeast of Los Angeles since January. Before arriving there, Lindh had been held at a federal lockup in Virginia. He was moved to be closer to his parents, who live in Northern California.
Lindh was placed in the general prison population last month at his attorneys' request and was working as an orderly, cleaning indoors where guards could watch him, the Sun reported, citing an unidentified prison source. The source said that since Monday, Lindh had been in special housing, similar to solitary confinement, for his protection.
Federal Bureau of Prisons spokesman Dan Dunne said Lindh "is housed in a unit which is consistent with his individual safety and security needs."
The prison has more than 1,650 inmates.