The United States has warned Greece any effort to assist the passage of an Iranian tanker towards Syria would be viewed as support for a terrorist organisation.
It is heading to the Greek port of Kalamata, according to ship-tracking service MarineTraffic, with US officials saying it has millions of dollars of oil on board.
The Adrian Darya 1, previously named Grace 1, had been held in Gibraltar.
The vessel left Gibraltar late on Sunday after having been detained for a month in the British overseas territory for allegedly trying to breach European Union sanctions on Syria.
Gibraltar authorities rejected attempts by the US to seize the oil tanker again, arguing that EU regulations are less strict than US sanctions on Iran.
Gibraltar said it had been assured by Iran that the tanker would not unload its cargo in Syria.
Iranian government officials have yet to publicly acknowledge the ship's next destination, or where it will discharge its cargo of 2.1 million barrels of crude oil. Iran has denied it was ever headed for Syria.
The tanker's release comes amid a growing confrontation between Iran and the West after US President Donald Trump pulled Washington out of Tehran's nuclear deal with world powers over a year ago.
Shortly after the tanker's detention in early July, Iran seized the British-flagged oil tanker Stena Impero, which remains held by the Islamic republic.
Analysts had said the Iranian ship's release by Gibraltar might mean that the Stena Impero could go free.
But Iranian officials denied there was any link between the two ships.