The 37-year-old was detained after flying in from the Turkish city of Istanbul yesterday, police said in a statement.
The passport was one of a batch of blank travel documents seized by IS fighters during a raid in Nineveh province, and subsequently cancelled by Iraqi authorities, the statement added. Police did not say when the raid took place.
Greek police routinely uncover false or illegal travel documents among migrants hoping to reach northern or western Europe.
A European Union report compiled in November said Greece was failing to properly register and fingerprint migrants, but Athens insists the situation has drastically improved with the arrival of additional EU staff and registering equipment.