The ferry ran into trouble about 40km off Mandalika island, 300km northeast of the capital, Jakarta.
Hatta Radjasa, the transport minister, put the number of passengers at 542, citing the passenger manifest.
However, ships in Indonesia often carry far more passengers than recorded, making it hard for authorities to say with accuracy how many people were on board.
Two naval ships were searching the area, but found nothing due to poor visibility. Local fishermen were reportedly too scared to head out into the stormy seas.
Ships and ferries are a popular means of transport among Indonesia's 17,000 islands, where sea connections are cheaper and more available than air routes, but safety standards are not strictly enforced.