Karya Indah Vessel was carrying at least 40 passengers when it sank near Samarinda City at about 6:15 p.m. Wednesday, the Antara news agency reported.
The National Disaster Mitigation Agency said a leak in the vessel's hull was what caused it to sink.
So far, 17 passengers have been discovered alive and one person has been confirmed dead from the incident.
"Several victims have returned to their homes, two other persons are hospitalized at IA Moeis Hospital, while one person is treated at Traumatic Center," said a medical official at the Traumatic Center.
Meanwhile, at least 22 other passengers have been reported missing.
A search and rescue team from the Mobile Brigade, the East Kalimantan and Samarinda Regional Disaster Mitigation Agency, and local police have been monitoring the area in which the vessel sank for victims.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Exploding whale video goes viral on Internet