Among the buildings damaged by the 6.6 magnitude temblor were mosques, schools, homes and government buildings.
Residents of Singkil, an area near the epicenter, said utility poles fell and crashed into houses during the shaking.
The U.S. Geological Survey said the quake struck at 12:55 a.m. local time about 60 miles southwest of the city of Medan, and 250 miles southeast of the provincial capital of Banda Aceh.
One of the victims was a young boy in the Simpang Kiri sub-district who was crushed by bricks from a collapsing wall as he slept next to his mother.
Two other people were killed in separate incidents, according to the National Disaster Management Agency.
Aceh was devastated by a 9.1 magnitude quake centered off western Sumatra on Dec. 26, 2004, which also triggered a huge tsunami that killed more than 220,000 people around the Indian Ocean.