At about 7:45 this morning, Roof was near the showers when another inmate, Dwayne Stafford, left his cell, ran down a set of stairs and toward Roof and assaulted him, officials said.
Charleston County Sheriff Al Cannon said Stafford, 25, punched Roof, 22, "a number of times and assaulted him quickly."
Roof was hit in the face and body and suffered bruising to his face and back, the incident report states. Detention officers intervened.
The incident report calls the assault "unprovoked," and Roof and Stafford were "checked by medical at the jail and cleared," the report states.
Roof's injuries were "relatively minor," Cannon said, and he was not hospitalized, a jail representative said.
Stafford is serving time for strong-arm robbery and assaulting a police officer, Cannon said. An arrest warrant for Stafford is expected. Cannon said Roof and his attorney have no desire to press charges against Stafford.
The investigation is ongoing, and Cannon did not say what sparked the incident. He said Stafford should not have been able to get out of his cell, and how that happened is among the issues being investigated. Cannon added the assault did not seem "coordinated."
Roof, who is accused of murder and hate crimes, faces a federal trial set for November and a state trial set to begin early next year. He could face the death penalty in both cases.
His state and federal attorneys have said he is willing to plead guilty in exchange for a life sentence.
The Associated Press contributed to this report.