The Sriwijaya Air Boeing 737 lost contact en route to Pontianak in West Kalimantan province, officials said.
Flight tracking website Flightradar24.com said the aircraft had lost more than 3,000m (10,000ft) in altitude in less than a minute.
The transport ministry said search and rescue efforts were under way.
Sriwijaya Air, a local carrier, said it was still gathering information about the flight.
The plane is not a 737 Max, the Boeing model involved in two major crashes in recent years.
The first of those, in October 2018, involved an Indonesian Lion Air flight which plunged into the sea killing 189 people.