Justice Ministry spokesman Busho Ibrahim said Oras Muhammad Abdul-Aziz was executed by hanging on July 3.
Iraq's Central Criminal Court in 2006 handed down a death sentence to Abdul-Aziz for his role in the August 2003 bombing of the Imam Ali shrine in Al-Najaf.
The blast killed at least 85 people, including leading moderate Shi'ite cleric Ayatollah Muhammad Baqir al-Hakim, then the head of the Supreme Council for the Islamic Revolution in Iraq (SCIRI).
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SUNNI, SHI'A: Iraq is riven along sectarian lines, faults that frequently produce violent clashes and are a constant source of tension. Sectarian concerns drive much of Iraqi politics and are the main threat to the country's fragile security environment.