The Sriwijaya Air disappeared from radars four minutes into its journey to Pontianak in West Kalimantan province.
It is thought to have dropped more than 3000m in less than a minute, according to flight tracking website Flightradar24.com.
Witnesses said they had seen and heard at least one explosion.
Fisherman Solihin, who goes by one name, told the BBC Indonesian service he had witnessed a crash and his captain decided to return to land.
"The plane fell like lightning into the sea and exploded in the water," he said.
