The Euroferry Olympia had 239 passengers and 51 crew members on board when it caught fire northeast of the island of Ericosa, near Corfu, leading to the evacuation.
The Coast Guard said 278 people were rescued – including an individual who was not on the official passenger list.
According to Reuters, most of the passengers boarded rescue ships and were taken to the neighboring island of Corfu, where they were then registered.
The Greek coast guard said in the statement that the two people still trapped on the ferry were foreign nationals.
Eight of the 11 missing passengers are also foreign nationals, while three are Greek nationals.
The ship was sailing under the Italian flag and was on its way from Igoumenitsa in northwestern Greece to Brindisi in southern Italy when it caught fire.
The Coast Guard received a call about the fire on the ship around 4:30 a.m. local time.
A spokesperson for Grimaldi Lines, the owner of Euroferry Olympia, told Reuters that while the cause of the fire was under investigation, there were indications that it started inside the ship’s hold.
A video posted on the Greek news website Proto Thema showed a 600-foot (183-meter) ferry set ablaze amid plumes of smoke. Labor Day was blasting from the loudspeakers.
Greek public radio station ERT showed live images of boats carrying passengers arriving at the port of Corfu.
Speaking at ERT, Corfu Hospital Director Leonidas Rubatis confirmed that three passengers with minor injuries were brought in as a precaution, and that the infant was also expected to be examined as a precaution.