A spokesman, confirming a report in Dong-A Ilbo newspaper, said the South's navy on Saturday detained the five-ton boat about 1.6 miles (2.5 km) south of the disputed border.
Officials were interrogating the group, the spokesman told AFP. "None of them has yet expressed an intention to defect."
The incident off the frontline island of Yeonpyeong comes at a sensitive time as the two Koreas prepare for their first talks since the North's deadly shelling of the island in November.
The 11 men and 20 women arrived off the island in thick fog and were towed to the western port city of Incheon, Yonhap news agency quoted a military official as saying. The official described them as members of a work group and not family members. There were no children on board.
"Given the circumstances so far, they might have been drifting after setting the wrong coordinates or losing power on their boat," another official was quoted as saying. The contested Yellow Sea border has been a persistent flashpoint. The North's shelling of Yeonpyeong, which killed two marines and two civilians, briefly sparked fears of war.
The two sides will hold preliminary military talks Tuesday to try to ease months of tensions. On December 25, a North Korean crossed the border by boat and landed on Baengnyeong, another frontline island. He was allowed last month to return to the North after expressing a wish to do so.
More than 20,000 North Koreans have arrived in South Korea since the end of the 1950-53 war, mostly via China.