A National Search and Rescue Agency team preparing to search the crash area.
The transport ministry had initially said there was a total of 188 people on board.
The flight took off from Jakarta around 6.20am and was due to have landed in Pangkal Pinang, capital of the Bangka-Belitung tin mining region, an hour later.
Search and Rescue Agency spokesman Yusuf Latif said authorities were still searching for the remains of the plane, which lost contact with air traffic control around 6.30 am (2330 GMT).
A spokesman for DFAT said the Department of Foreign Affairs and Trade was aware of the reports. The plane crashed into the sea about 13 minutes after takeoff.
Indonesia's Air Force says it has deployed three helicopters for search and evacuation in the waters of Tanjung Karawang.
"We don't know yet whether there are any survivors", Search and Rescue Agency head Muhmmad Syaugi told reporters. The flight was traveling from Jakarta to Depati Amir airport in Pangkal Pinang. "I wouldn't expect a catastrophic technical fault to be the cause of this crash in Indonesia and I absolutely do not believe it should be cause for concern about the overall safety of this type of aircraft".
"The weather was also good, everything was clear before the incident", he added. According to The Straits Times as quoted by news agency ANI, the plane had requested a return to base before disappearing from radar.
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Sindu Rahayu, directorate general of Civil Aviation at the transport ministry, said the aircraft was carrying 178 adult passengers, one child and two babies, with two pilots and five flight attendants.
Aviation tracking website Flightradar24 says the Lion Air plane that crashed after takeoff from Jakarta was a brand-new aircraft that has only been in use for a couple of months. "Most unfortunate that Indian Pilot Bhavye Suneja who was flying JT610 also lost his life", Indian Embassy in Indonesia said in a tweet.
Lion Air has confirmed that the aircraft had a "technical problem" on the previous flight, "which had been resolved according to the procedure".
Lion Air, a discount carrier, is one Indonesia's youngest and biggest airlines, flying to dozens of domestic and global destinations. Lion had operated 11 Boeing 737 MAX 8s and it had no plan to ground the rest of them, he said.
The plane dropped more than 500 feet (152 metres), veered to the left and then started climbing again to 5,000 feet (1,524 metres). Last year, it served almost 51 million passengers, six million more than in 2016.
On Facebook there are photos of him in his Lion Air uniform, smiling.
Before Monday's crash, the airline had not reported a fatal accident since 2004, when 25 people died after the DC-9 they were on, crashed amid heavy rain at Solo City in central Java.