The Australians are Elliot Foote, Steph Weisse, Will Teagle and Jordan Short, who were part of a group in a wooden speedboat in the waters around Sarang Alu and Banyak islands in Aceh Singkil district.
A total of 12 Australian nationals and five Indonesians were travelling to Pinang Island in two boats.
The area is known as a tourist destination with white sand beaches and good waves for surfing.
The boats left North Nias port in Nias island, which located around 150km from Indonesia's Sumatra island on Sunday afternoon and experienced bad weather with very heavy rain during the trip.
Ten of them decided to stay and shelter on Sarang Alu island, while the others continued the trip, Nias Search and Rescue Agency said in a statement on Monday.
The resort on Pinang Island later reported to the agency that the boat with 10 passengers had safely arrived, but the boat that had left earlier had not been seen.
Rescuers were sending at least two rescue boats and a medical boat to the search area.
The Department of Foreign Affairs and Trade confirmed it was working closely with Indonesian authorities to support search and rescue efforts.
The department was also providing consular assistance to the four families, a spokeswoman told AAP.
On Monday night, the families of the missing Australians issued a statement saying they were holding out hope they will be found.
"Our hearts are aching at the thought that Elliot, Steph, Will and Jordan are missing at sea. We continue to pray and hold out hope they will be found," it said.
"We'd like to thank the Indonesian authorities and the Australian government for their ongoing assistance while search and rescue efforts continue."
Indonesia is an archipelago with more than 17,000 islands, and ferries and boats are a common form of transportation. With lax safety standards and problems with overcrowding, accidents occur frequently.
In July, an overloaded passenger boat capsized off Indonesia's Sulawesi island, killing 15 people.
In 2018, an overcrowded ferry with about 200 people on board sank in a lake in North Sumatra province, killing 167 people. In one of the country's worst recorded disasters, an overcrowded passenger ship sank in February 1999 with 332 people aboard. Only 20 people survived.
with AAP
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