Flight JT 610 was headed for Pangkal Pinang, in the Bangka Belitung Islands, when it lost contact and is believed to have ended up under water.
No survivors have been found.
The plane was a new type of aircraft and it is unclear what caused the crash. Lion Air is Indonesia’s largest low-cost carrier.
“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.”
Items believed to belong to passengers have been found in the water, including ID cards and driver’s licences, the search and rescue agency said on Twitter.
“We don’t know yet whether there are any survivors,” the agency’s head, Muhmmad Syaugi, told reporters.
“We hope, we pray, but we cannot confirm.”
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, there are conflicting reports on the exact number of people on board.
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.
The head of Indonesia’s disaster agency, Sutopo Purwo Nugroho, has tweeted images which he said showed debris and personal belongings that came from the aircraft and had been found floating in the sea.
He also shared a video he said had been taken from a tugboat off Karawang, just east of Jakarta, which appeared to show floating debris and an oil slick.
Debris was also seen near an offshore oil refinery operated by state-owned energy firm Pertamina, an official from the firm said.
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 those on board were trainee flight attendants and one was a technician.
At least 20 employees from Indonesia’s finance ministry were 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.
The aircraft was a Boeing 737 MAX 8, a model only in commercial use since 2016.
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.
Edward Sirait, chief executive of Lion Air Group, told Reuters: “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.”
The plane had had a technical problem on a previous flight, he said, but it had been resolved “according to procedure”.
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.
Indonesia, a vast archipelago, is heavily reliant on air travel, but many of its airlines have a poor safety record.
Established in 1999, Lion Air operates flights domestically as well as a number of international routes in South East Asia, Australia and the Middle East.
It has had issues of safety and poor management in the past and was banned from flying into European airspace until 2016.
In 2013, Lion Air flight 904 crashed into the sea on landing at Bali’s Ngurah Rai International Airport. All 108 people on board survived. In 2004, flight 538 from Jakarta crashed and broke up on landing at Solo City, killing 25 people.
In 2011 and 2012 there was a spate of incidents where pilots were found in possession of methamphetamines, in one incident hours before a flight.