The video shows former intelligence chief Barzan Ibrahim al-Tikriti and Awad al-Bandar, the former head of Iraq's Revolutionary Court, standing side by side on what appears to be the same gallows where Hussein was hanged on December 30.
They are wearing hoods and orange prison jumpsuits.
The video also shows al-Tikriti's head being ripped from his body by the noose in what government spokesman Ali al-Dabbagh said was a "rare" incident.
"There was no violation of procedure, no chants, and no insults were directed to the convicts, and the convicts were not subjected to any mistreatment," al-Dabbagh said. "In a rare case, the head of Barzan was detached from his body during the execution. Relatives of the two mentioned will be notified by official governmental authorities and they will be requested to collect their bodies."
Al-Dabbagh said all laws and rules were respected during the executions.
Video of Hussein's execution prompted widespread condemnation as it showed the former dictator being taunted on the gallows.