The 10-meter vessel was travelling from North Nias Island to Aceh's Banyak Island.
The boat lost contact at around 6 p.m. on Sunday.A search was under way on Monday but the operation was called off as night fell.
A search was under way on Monday but the operation was called off as night fell.
"We will continue the search operation on Tuesday morning," the head of Nias's rescue agency, Oktavianto, told Reuters.
The four tourists were among a group of 12 Australians travelling to Banyak Island. The other eight were in another boat.
Accidents involving boats are common in Indonesia, an archipelago of more than 17,000 islands, as lax safety standards often allow vessels to be overloaded without adequate life-saving equipment.