Many of the missing are high school students, who boarded the ferry, named Sewol, in the port of Incheon on their way to the holiday island of Jeju.
Six people are confirmed dead, including three 17-year-old students and a crew member.
South Korean officials said that 179 people had been rescued so far. Some of them climbed to the top of the sinking ship, while others jumped into the water and were picked up by commercial or military vessels.
"I had to swim a bit to get to the boat to be rescued," one of the high school students told YTN. "The water was so cold and I wanted to live."
South Korean Prime Minister Chung Hong-won said there was not "a minute or a second to waste" in the rescue efforts.