Some 39 passengers have been rescued so far off the coast of the West African nation, police official Ibrahim Samura said.
At least 221 people remain missing and some of the passengers also were traveling with young children, Samura said.
"Most of the passengers were school-going children returning from holidays," Samura said.
The boat was traveling from the village of Shenge to Tombo, near Freetown, when the accident occurred Wednesday.
"On the day of the accident the sea was rough and it was windy," Samura said, adding that the boat also may have capsized because of overloading. In addition to the at least 268 people aboard, the Teh Teh also was carrying other goods.
The boat has been found afloat, Samura said, and search and rescue operations were continuing in the area.
Sierra Leone is in the middle of its rainy season, with persistent and heavy storms affecting both land and sea.
Boat accidents are also common in West Africa, where road systems are poor and many people rely on rickety watercraft to move their wares to market.