The Lebanese officials, close to the Shiite Hezbollah, say Ibrahim Mohammed al-Haj was killed during the past week while on a "jihadi mission" without providing further details.
It is the first known Hezbollah death in Iraq since Sunni extremists captured large parts of the country north and west of Baghdad in June.
The officials spoke on condition of anonymity because of the sensitivity of the matter.
Iraqi officials have said that a handful of advisers from Hezbollah are offering front-line guidance to Iraqi Shiite militias fighting jihadi militants north of Baghdad.