The announcement on Monday follows an administrative investigation ordered by Lieutenant General Ricardo Sanchez, the commander of US forces in Iraq, into abuse of Iraqis at Abu Ghraib.
Six other soldiers are already being criminally investigated for their involvement in the alleged abuse.
The reprimands are private and no details will be released on the names or ranks of those punished, the US official said.
A seventh person received a lesser letter of admonishment in connection with the same incident.
Last week, the US network CBS released pictures of US soldiers abusing and humiliating prisoners inside Abu Ghraib, including piling them up naked and hooded.
A prisoner was made to stand on
a box with electric wires attached
In one case a prisoner standing on a box had wires attached to his hands and feet and was told he would be electrocuted if he stepped off it.
Sanchez ordered an investigation into possible abuse in January, and in March the US military brought charges of assault, cruelty and maltreatment against six soldiers, members of a military police battalion.
The alleged abuses were said to have involved about 20 prisoners and took place in November and December last year.
Sanchez's non-criminal, administrative investigation was launched at the same time as the criminal probe.
A second administrative investigation into "interrogation practices used in Abu Ghraib" is also underway and follows reports that intelligence officers may have encouraged the abuse.
Britain is investigating separate allegations of abuse by British troops in southern Iraq.