Officials said that a search and rescue operation is underway.
Edward Sirait, chief executive of Lion Air Group said, "We can not give any comment at this moment".
Lion Air JT610 pilot Bhavye Suneja. They routinely took this flight.
At least 23 government officials were on board the plane, which an air navigation spokesman said had sought to turn back just before losing contact.
Sony Setiawan, an official in Indonesia's finance ministry, had meant to be on board the ill-fated flight JT610, a journey he and his colleagues caught on a weekly basis.
Indonesian TV broadcast pictures of a fuel slick and debris field.
Engine maker CFM International says it's standing by to offer assistance to Lion Air, CNBC reported, citing a company statement.
What do we know about this aircraft?"It was around two nautical miles from the co-ordinates given by air traffic control", Mr Syaugi said. We are there already - our vessels, our helicopter is hovering above the waters to assist. "We are trying to dive down to find the wreck". "Hopefully the process would not take long".
Lion Air's flight JT-610 was heading to Pangkal Pinang, an island north of Indonesia's capital. "Our team has been deployed", Mr Latif said.More news: These companies spent millions on political adds on Facebook
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Lion Air is a budget airline based in the country.
Flight JT 610 took off from Jakarta at 06:20 local time on Monday morning (23:30 GMT on Sunday).
- The Boeing 737 MAX was expected to land in Pangkal Pinang on Monday 7.20am. The disaster agency of Indonesia has released some images which shows the debris and belongings that were floating in the Java sea after the plane sank into it.
It says final telemetry from the aircraft indicates it was in a "rapid descent".
A Boeing 737 passenger plane has crashed after taking off from Jakarta's global airport, with 188 people feared dead.
Two infants are among those missing on the aircraft.
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.
"Boeing is aware of reports of an airplane accident and is closely monitoring the situation", the manufacturer tweeted.
Just six months ago, a Lion Air plane skidded off the runway at Djalaluddin Airport in Gorontalo, Indonesia. The carrier operates an extensive network of domestic and global passenger and cargo services using mainly Boeing 737s. However, there are conflicting reports on the exact number of people on board.
Indonesia, a vast archipelago, is heavily reliant on air travel, but many of its airlines have a poor safety record. According to an official, Lion Air flight was carrying 188 people, including crew.