The budget carrier has been involved in a number of incidents including a fatal 2004 crash and a collision between two Lion Air planes at Jakarta's Soekarno-Hatta airport.
The minister also said fares provided by low-cost carriers will be evaluated, saying they are frequently too low and excessive cost-cutting could indirectly affect flight safety.
All 189 people on board are believed to have died in the crash.
Also, Indonesian investigators searching for the flight recorders of the crashed plane said that they heard transponder "pings" that could lead them to the devices, and answer questions as to why the new Boeing 737 MAX 8 went down.
A commercial airliner jet's "black box" - the data recorder that facilitates aviation accidents - is located in the fuselage. Later in the flight, a man who was either the captain or first officer walked through the plane and returned to the cockpit with what looked like a large manual.
The AP said the data from Sunday's flight was similar to preliminary data from Monday's flight, though it described safety experts as saying accuracy should be checked against the plane's so-called black boxes, which would contain information about the final moments aboard the plane and are expected to be recovered.
All 189 were feared dead as only body parts and plane debris have been found so far in waters off the province's Karawang regency.
Lion Air said there were reports of technical problems with Sunday's flight from Bali, but they had been resolved in accordance with the plane manufacturer's procedures.
Lion Air pledged to assist her family with their needs and provide compensation.
Officials from Boeing are meeting the Indonesian authorities on Wednesday as part of the investigation.
Shares of Boeing have almost completely rebounded after dropping nearly 7% shortly after the news broke.
Luckily that flight was able to land safely in Jakarta.
Forensic experts identified Jannatun Cintya Dewi, a civil servant working in Indonesia's Ministry of Energy and Mineral Resources, as the first victim of the crash on Wednesday evening.
"He was the best husband in the world", 33-year-old Ningsi Ayorbaba said of her partner Ferdinand Paul Ayorbaba, who was on the flight. Officials said the pilot and co-pilot had a combined 11,000 hours of flying experience.
This was because search teams had detected consistent "ping" signals with 0.9-second intervals from what could be the flight recorders.
Debris, personal items, including 52 identification cards and passports, and body parts were found offshore yesterday.
Divers conduct an operation near the search area of a site where Lion Air flight JT610 plane had crashed, off Tanjung Pakis, Indonesia, Wednesday, in this still image taken from a video obtained from social media.