The floods, which hit Indonesia almost a week ago, have killed 303 people - with the number expected to rise as more bodies are recovered - and displaced thousands.
The deluges triggered landslides, damaged roads, cut off parts of the island and downed communication lines.
The challenging weather conditions and the lack of heavy equipment also hampered rescue efforts.
Aid has been slow to reach the hardest-hit city of Sibolga and Central Tapanuli district in North Sumatra.
Videos on social media showed people scrambling past crumbling barricades, flooded roads and broken glass to get their hands on food, medicine and fuel.
Some even waded through waist-deep floodwaters to reach damaged convenience stores.
North Sumatra Police first reported incidents on Saturday evening, police spokesperson Ferry Walintukan said, adding regional police had been deployed to restore order.
"The looting happened before logistical aid arrived," he said.
"(Residents) didn't know that aid would come and were worried they would starve."
Eleven helicopters were deployed from Jakarta to the affected areas the day after the disaster for ongoing logistics distribution operations, especially to places where land access was cut off, Cabinet Secretary Teddy Indra Wijaya said on Sunday.
"But unpredictable weather often hampers aid operations," he said.
The Cabinet Secretariat released footage of the military airdropping supplies to the affected areas.
In the village of North Tapanuli, survivors waved frantically to the helicopters carrying aid. Meanwhile, four navy ships docked at a port to support aid distribution.
Authorities in Sri Lanka said the death toll from floods and mudslides had risen to 193, with 228 others still missing.
Almost 148,000 people have been displaced from their homes and are housed in temporary shelters.
Sri Lanka has been battered by severe weather since last week.
Conditions worsened on Thursday, with heavy downpours that flooded homes, fields and roads and triggered landslides in the tea-growing central hill country.
Authorities say Cyclone Ditwah, which developed in the seas east of Sri Lanka, is likely to move toward India's southern coast on Sunday.
