According to the report, the Lion Air flight (JT-610) took off from Jakarta airport at 6.20am local time. It wasn't clear how many passengers and crew were on board.
There's no word on casualties yet.
Debris, including plane seats, have been found near its offshore facility in Java sea, Indonesia energy firm Pertamina official said.
The Lion Air 737 Max-8 went missing about 10 minutes after taking off from Jakarta's global airport.
Lion Air, which flies to 126 destinations in Indonesia, Malaysia, Saudi Arabia and China, is the second largest low-priced carrier in south-east Asia (after Malaysia's AirAsia), and it's growing fast.
Lion Air Group's Chief Executive Edward Sirait earlier told Reuters: "We can not give any comment at this moment". "We're trying to dive to locate the plane", Syaugi said.
"A few flakes of Lion Air plane that crashed in waters of Karachi", he wrote in the first tweet, accompanying the photos.
The BBC reports Indonesian aviation officials have confirmed Lion Air Flight JT610 crashed into the sea.
"The Department of Foreign Affairs and Trade is aware of reports of the missing Lion Air aircraft in Indonesia".
Preliminary flight tracking data from Flightradar24 shows the aircraft climbed to around 5,000 feet (1,524 m) before losing, and then regaining, height, before finally falling towards the sea.
Information gathered by the Jakarta Post said that the plane, Lion Air 610, took off from Jakarta at 6.20 a.m. and contact was lost at 6.33 a.m.
The aircraft is reportedly a Boeing-737 Max 8, capable of seating up to 210 passengers.
Lion Air airline has confirmed that the plane went off the radar on Monday morning.
The plane was a Boeing 737 MAX 8, a brand new type of aircraft.
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