Staff Sgt Joseph Chamblin pleaded guilty at a special court martial to "dereliction of duty" for failing to supervise junior marines and wrongfully urinating on a deceased enemy combatant.
He was initially given 30 days in jail but a plea bargain spared him incarceration.
The YouTube footage, which is less than one minute long, shows Chamblin and Staff Sgt Edward Deptola, in uniform, urinating on three Taliban corpses. One of the men chuckles as they do so while another says, "Have a great day, buddy".
The Marine Corps said the incident happened during a counter-insurgency operation in the Musa Qala district of Helmand province in July 2011.
The video is likely to have aggravated anti-American sentiment in Afghanistan after a decade-long war which has seen several other cases of abuse, notably in the notorious Abu Ghraib prison in 2004.
Afghanistan's President Hamid Karzai condemned the actions in the video as "inhuman".
Chamblin was charged with failing to properly supervise junior marines, failing to to report misconduct, failing to report the negligent discharge of a grenade launcher, and failing to stop the indiscriminate firing of weapons, the Marine Corps said.