Flight JT 610 was headed for Pangkal Pinang, in the Bangka Belitung Islands, when it lost contact.
Rescuers have recovered some remains and there is no sign of survivors.
The cause of the crash, involving a new plane in operation since August, remains unclear. Lion Air is Indonesia’s largest low-cost carrier.
The incident is reported to be the first major accident involving a Boeing 737 Max – an updated version of the 737.
“The plane crashed into water about 30m to 40m deep,” Search and Rescue Agency spokesman Yusuf Latif told AFP news agency. “We’re still searching for the remains of the plane.”
Rescuers have recovered body parts from the sea. Items believed to belong to passengers have also been found in the water, including baby shoes, ID cards and driver’s licences.
“We need to find the main wreckage,” Bambang Suryo, operational director of Indonesia’s search and rescue agency said. “I predict there are no survivors, based on body parts found so far.”
At an earlier news conference, officials said the plane had been carrying 178 adults, one infant and two babies, as well as two pilots and five cabin crew. However, Lion Air has since named six cabin crew.
Distraught family members of those on board have been gathering at Jakarta’s Halim Perdanakusuma Airport as they wait for news.
Flight JT 610 took off from Jakarta at 06:20 local time on Monday morning (23:30 GMT on Sunday).
It was due to arrive at Depati Amir airport in Pangkal Pinang an hour later but 13 minutes into the flight, authorities lost contact with the plane.
The pilot had asked to return to Jakarta’s Soekarno-Hatta airport, the head of Pangkal Pinang’s search and rescue office, Danang Priandoko, told local news outlet Kompas.
How could a brand new plane crash?
Images from the Lion Air plane crash
Lion Air Chief Executive Edward Sirait has said the plane had an unspecified “technical issue” on a previous flight, but he said that this had been “resolved”.
The airline operates 11 Boeing 737 Max 8 planes but the others have not had a similar technical problem and there is no plan to ground the fleet, he said.
What do we know about those on board?
Lion Air said in a statement that the pilot and co-pilot were experienced, with more than 11,000 flight hours between them.
Three of the crew on board were trainee flight attendants and one was a technician.
Twenty employees from Indonesia’s finance ministry were also on board, the BBC has learned.
A spokesperson for Indonesia’s finance ministry Nufransa Wira Sakti said they worked at the finance ministry offices in Pangkal Pinang but had been in Jakarta for the weekend. They routinely took this flight.
What do we know about this aircraft?
The aircraft was a Boeing 737 MAX 8, a model only in commercial use since 2016. The 737 Max series are the fastest-selling planes in Boeing history, and there are four models – the Max 7, Max 8, Max 9 and Max 10.
Nearly 4,700 orders have been taken from around the world, according to Boeing.
Lion Air said the aircraft involved in the crash was made in 2018 and has only been operated by the airline since 15 August this year.
It is a single aisle plane used for short-haul travel.
Mr Sirait told Reuters news agency: “We don’t dare to say what the facts are, or are not, yet.
“We are also confused about the why, since it was a new plane.”
In a statement, Boeing expressed sympathy for the victims and families and said it “stands ready to provide technical assistance to the accident investigation”.
Australia told government workers and contractors to stop using the airline until the findings of the investigation were out.