The first undersea tremor hit at 7:14 am (0014 GMT) and was centered at a depth of 31 kilometers (19 miles), 84 kilometers west of the provincial capital Banda Aceh, said Agus, an official at the meteorology office in Jakarta.
A second quake had a magnitude of 5.2 and hit at 2:24 pm (0724 GMT). It was centered at a depth of 67 kilometers, 198 kilometers southwest of Sinabang, the main town on Aceh's Simeulue island, said Eva, another official from the office.
Both said there were no immediate reports of damage or casualties.
Indonesia sits on the Pacific "Ring of Fire", where the meeting of continental plates causes high volcanic and seismic activity.
A 6.3-magnitude earthquake struck the city of Yogyakarta and its surroundings on the island of Java on May 27 and killed 5,855 people.
Indonesia's Aceh province was the hardest hit by a 9.3-magnitude quake off the coast of Sumatra that triggered tsunamis in December 2004. The waves killed more than 220,000 people around the Indian Ocean.