Of 40 passengers on board, 19 were still missing, while six survived, the agency said in a statement. The cause of the sinking, which occurred at about midnight, was still unclear.
"All the victims have been identified and handed over to the families while the survivors are now being treated in local hospitals," said Muhamad Arafah from the local branch of the search and rescue agency.=
Photos shared by the rescue agency showed victims' bodies covered in cloth on the floor of the local hospital.
The vessel was ferrying people across a bay in Muna island, about 200 km (124 miles) south of Kendari, the capital of Southeast Sulawesi province.
Ferries are a common mode of transport in Indonesia, an archipelago of more than 17,000 islands, and accidents are common as lax safety standards often allow vessels to be overloaded without adequate life-saving equipment.