On board the Euroferry Olympia were 239 passengers and 51 crew members, according to a Coast Guard statement.
There were no immediate reports of deaths or serious injuries.
The ship was sailing under the Italian flag and was northeast of the island of Ericosa near Corfu when the fire broke out.
She was on her way from Igoumenitsa in northwestern Greece to Brindisi in southern Italy.
The Coast Guard received a call about the fire on the ship around 4:30 a.m. local time.
According to Reuters, most of the passengers boarded rescue ships and were taken to the neighboring island of Corfu.
In a press release Friday, the Greek Coast Guard said the process of registering and identifying the rescued passengers was underway.
A video posted on the Greek news website Proto Thema showed the 600-foot (183-meter) ferry ablaze amid plumes of smoke. Labor Day was blasting from the loudspeakers.
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.
The Greek public station ERT showed live images of boats carrying passengers and arrived 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.