The Greek-flagged ship Sounion has been on fire since Aug 23 after an attack by Yemen's Houthis in Red Sea. The EU mission published photos showing fire and smoke coming out of the vessel's main deck.
Though the tanker is carrying 150,000 tonnes of crude oil, there have been signs of oil spill.
If the spillage occurs, it could cause a major environmental disaster.
The vessel was attacked 140 kilometres off the coast of Yemen’s Hodeida city.
The 29-member crew escaped unharmed and were evacuated by a French naval vessel.
Houthis has been attacking ships in solidarity with Palestinians in the war between Israel and Hamas in Gaza.