The blaze on the Euroferry Olympia prevented rescuers from boarding, but tugboats managed to tow the vessel closer to the island, ERT television said.
The ferry on Saturday afternoon was just some 6 nautical miles (around 11 km) north of Corfu, ERT said, after anxious relatives started arriving in the morning.
A thick cloud of black smoke billowed into the sky after wind rekindled the fire, with Greek state agency ANA reporting the heat onboard had reached 500 degrees Celsius.
The coastguard has said those missing were all lorry drivers -- seven from Bulgaria, three from Greece, one from Turkey and one from Lithuania.
On Friday, 280 passengers were evacuated to Corfu after a blaze broke out the previous night as the Olympia was en route from Greece to Italy.
Rescuers who boarded the burning vessel halted work Friday evening because of the intense heat, dense smoke and darkness, ANA said.
One of the rescuers was taken to hospital with respiratory problems but was released on Saturday, the fire brigade told AFP.
The cause of the fire remains unknown.
Shipping minister Giannis Plakiotakis said a team from the Maritime Accident and Incident Investigation Service was in the area to launch a probe.
ERT reported the vessel's captain and two engineers had on Saturday been brought before a prosecutor.
Plakiotakis told Skai television that, after the fire is extinguished, the ferry would be towed to safety in order to pump out any fuel, and avoid marine pollution.
Rescued truckers told Greece's public broadcaster some drivers had preferred to sleep in their vehicles because the cabins were overcrowded.
According to the Kathimerini newspaper, the Greek trucker union had since June 2017 warned about conditions on the Olympia as well as another ferry belonging to Italian ferry and container operator, Grimaldi.
Ilias Gerontidakis, the son of a missing Greek trucker, told the Proto Thema online newspaper the Olympia "miserable from every point of view".
"It had bed bugs, it was dirty, it had no security systems," said the young truck driver, as he waited in the port for news.
"It had 150 lorries inside. Normally it should have 70 to 75 cabins, but it only has 50. They force us to sleep four people in a cabin", he said. "My father, from what I was told, slept in the truck."
Vassilis Vergis, the cousin of another missing driver, said he thought his relative too "was afraid of the cabins".
"He probably stayed in the truck because he was afraid of coronavirus," he added.
The ferry's operator has claimed the 27-year-old vessel had last completed a safety check on February 16.
The ferry was officially carrying 239 passengers and 51 crew, as well as 153 trucks and trailers and 32 passenger vehicles, the company has said.
But the coastguard has said two of the people rescued -- both Afghans -- were not on the manifest, sparking fears that more undocumented passengers could also be missing.
The Bulgarian foreign ministry said 127 of its nationals were on the passenger list, including 37 truck drivers.
Another 24 were from Turkey, the country's NTV station said, while ERT said 21 Greeks were aboard.
Among the rescued, nine people remain in hospital with breathing difficulties.
Fahri Ozgen, a rescued passenger, recounted waiting for four hours for rescuers to arrive, as the flames roared around him.
"Two-hundred and fifty people were screaming, shouting, some of them were jumping into the sea," he told AFP.
"Some of our friends are still missing, we don't know where they are."
Turkish trucker Ali Duran said he had lost everything in the fire
"We lost our money, we lost our passports, we lost all our administrative documents," he said.
"I don't even have a shoe to wear."
The last shipboard fire in the Adriatic occurred in December 2014 on the Italian ferry Norman Atlantic. Thirteen people died in that blaze.