Officials voiced concern over the fate of the 107 people unaccounted for, fearing that many may have been trapped as the vessel listed sharply before capsizing.
Dramatic television aerial footage showed terrified passengers wearing life jackets clambering into inflatable boats as water lapped over the rails of the vessel as it sank.
Many appeared to have been rescued by fishing and other commercial vessels who were first on the scene before a flotilla of coastguard and navy ships arrived, backed by helicopters.
The 6,825-tonne ferry, which had sailed out of the western port of Incheon on Tuesday evening, ran into trouble some 20 kilometres (13 miles) off the southern island of Byungpoong.
Coastguard officials said they had received a distress call at 9:00 am (0000 GMT). The weather conditions were described as "fine" with moderate winds and sea swell.
The cause of the accident was not immediately clear, although rescued passengers reported the ferry coming to a shuddering halt after hearing a loud noise -- indicating it may have run aground.
Photos broadcast on television showed the ship initially tilted by more than 45 degrees on the port side with helicopters flying overhead, and then fully capsized with only a small section of the stern showing above the water.
"So far, 368 have been rescued," Lee Gyeong-Og, the vice minister of security and public administration, told a press briefing in Seoul.
Lee said two people had been confirmed dead, including one female crew member, and added that a detachment of South Korean Navy SEALS were continuing to search the submerged ship.
One local official who had taken a boat to the site and arrived an hour after the distress signal was sent, said he was "very concerned" about those still unaccounted for.
"The ship was already almost totally submerged when I got there. A lot of people must have been trapped," the official, who declined to be identified, told AFP by phone.
The video footage showed passengers sliding down the steeply inclined side of the ferry and into the water, as rescuers, including the crew of what appeared to be a small fishing boat, struggled to pull them to safety on board.
The water temperature was cold at around 12.6 degrees Celsius (55 Fahrenheit).
Of the 448 passengers on board the ferry which had been bound for the southern resort island of Jeju, 324 were students travelling with 14 teachers from a high school in Ansan, south of Seoul.
There were 29 crew members manning the vessel, which was also carrying 150 cars.
"I heard a big thumping sound and the boat suddenly started to tilt," one rescued student told the YTN news channel by telephone.
"Some of my friends fell over hard and started bleeding. We jumped into the water and got picked up by the rescue boats," he said.
Distraught parents of the students gathered at the high school in Ansan, desperate for news.
There were chaotic scenes in the school's auditorium, with parents yelling at school officials and frantically trying to make phone calls to their children.
"I talked to my daughter. She said she had been rescued along with 10 other students," one mother told the YTN news channel.
"They said they had jumped into the water before getting rescued," she said.
Hundreds of ferries ply the waters between the South Korean mainland and its multiple offshore islands every day, and accidents are relatively rare.
However in one of the worst incidents, nearly 300 people died when a ferry capsized off the western coast in October 1993.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.