Sirhan Sirhan, the man convicted of the murder of Robert F. Kennedy, was jailed in a California prison, according to US media.
Authorities say the stabbing took place in a prison near San Diego on Friday afternoon.
In a statement, the California Department of Correction and Rehabilitation said "officers responded quickly" to the attack.
The victim, whose condition is stable, was not mentioned in the statement.
But citing unnamed law enforcement sources, many US media reports identify 75-year-old Sirhan as a victim.
Sirhan is serving a life sentence at the Richard J. Donovan Correctional Facility where the piercing was performed.
The suspect attacker, a fellow citizen, was put in isolation, according to TMZ, who first reported the attack.
The motive for the attack being investigated has not been disclosed by officials.
Who is Sirhan Sirhan?
Sirhan was convicted of murdering the hope of President Kennedy, who shot three times at the Ambassador Hotel in Los Angeles on June 5, 1
New York Senator, brother of former Democratic President John F. Kennedy, died in hospital 24 hours later.
He was later buried in Arlington Cemetery, near his brother John, who was killed in 1963.
In his 1969 trial, Sirhan was initially sentenced to death. Three years later, however, his sentence was commuted to life imprisonment when California briefly banned the death penalty.
Palestinian citizen of Jordan, Sirhan claims he has no recollection of the Kennedy shooting.  In a television interview, Sirhan said he felt betrayed by Kennedy's support for Israel in the 1967 Six Day War.