The National Search and Rescue Agency says debris spotted so far include aircraft parts, a handbag, driving license and national identity card.
The plane took off from Jakarta with 189 people on board and was heading to Pangkal Pinang on the island of Bangka, which lies east of Sumatra.
The head of Indonesia's transport safety committee said he could not confirm the cause of the crash until the recovery of the plane's black boxes, as the cockpit voice recorder and flight data recorder are known.
Swedish flight tracking service Flightradar24 reported that the airplane was a Boeing 737 that had been delivered to Lion Air in August.
A spokesman for Lion Air reportedly told local media the airline was trying to find information on the plane's location.
"A few flakes of Lion Air plane that crashed in waters of Karachi", he wrote in the first tweet, accompanying the photos.
The crash was first reported by Reuters citing an Indonesian search and rescue official.
Divers on the surface of the ocean off Karawang as the hunt for survivors of the Lion Air aircraft that disappeared from radar shortly after taking off from Jakarta.
Speaking to media about the accident, the CEO of Lion airlines Edward Sirait said: "We can not offer any comment at this moment". 737 Max-8 model. Lion Air said it will cooperate with authorities in relation to this incident.
The crash is the worst airline disaster in Indonesia since an AirAsia flight from Surabaya to Singapore plunged into the sea in December 2014, killing all 162 on board.
In 2013, a 737-800 operated by the budget carrier crashed into the water near an airport in Bali.
The low-priced airline has been involved in numerous crashes in recent years, but none as seemingly deadly as the one off the coast of Jakarta.
"We can not give any comment at this moment", Edward Sirait, chief executive of Lion Air Group, told Reuters. Lion Air has been on an aggressive expansion plan in recent years, including putting in an order for 50 of the Boeing 737 Max single-aisle planes.
In 2017, Indonesia's air traffic controllers association announced that the rate of take-off and landings in Jakarta permitted by state-run air navigation company AirNav was larger than the airport's capacity, thus increasing the likelihoood of accidents.