The station aired scenes from a video by the Army of Ansar al-Sunna group showing the Turk standing between two masked men.
Aljzeera said the group killed the two men after they "confessed" to have cooperated with US forces.
Aljazeera said they would not air the beheading video, which it said it had obtained from a website, because it was too gruesome.
The Army of Ansar al-Sunna has seized and killed several captives in the past, including 12 Nepali men, three Iraqi Kurds and an Iraqi contractor.
Earlier this month it seized a member of the Kurdistan Democratic Party (KDP) who it described as a "spy" working as a translator for the US army.