Forty people were treated for injuries including broken legs, head wounds and shock, though only four were admitted to hospital, hospital officials said.
The brand new aircraft had flown from Bandung, in West Java, and was about to land at Bali airport. "But it probably failed to reach the runway and fell into the sea," said Lion Air spokesman Edward Sirait.
He said there were 101 passengers and seven crew on board but would not comment on the cause of the crash. An investigation is under way.
Bali's police chief told local television that there were two foreign passengers.
"There was no sign at all it would fall but then suddenly it dropped into the water," passenger Tantri Widiastuti, 60, told Metro TV. "I saw holes in the floor of the plane … we were evacuated quickly."
She said she had been treated for minor cuts.
Budget carrier Lion Air is Indonesia's largest airline and is rapidly expanding.
The plane was delivered last month. The company has signed two record contracts with two world's top plane makers, Boeing (BA.N) and Airbus (EAD.PA). Last month, it signed a deal with Airbus for 234 passenger jets worth a $24 billion. Two years ago, it signed a deal with Boeing for 230 planes.
Indonesia has been struggling to improve its civil air safety after a string of deadly accidents. In 2007, Lion Air was among a number of Indonesian airlines banned by the EU for lax safety standards. The ban was progressively lifted, starting in 2009.
The runway at Bali international airport starts next to the sea. The island is Indonesia's main tourist destination, especially popular with Australians for its surfing.
TV footage showed the jet floating in shallow waters with a fractured fuselage and passengers in the water with life jackets.
According to the Aviation Safety Network, Lion Air planes have been involved in six accidents since 2002, four of them involving Boeing 737s. Only one of them, according to the site, resulted in fatalities. (Additional reporting by Trisha Sertori in Bali; Writing by Jonathan Thatcher; Editing by Nick Macfie)