Aftershocks measuring 5.5 and 5.3 hit shortly afterwards, Indonesia's meteorological agency said.
Rustam Pakaya, the head of the Indonesian health ministry's disaster centre, said only that "many buildings" were damaged.
Al Jazeera's correspondent in Jakarta, Step Vaessen, said many residents had fled in panic to high ground following the quake, fearing a repeat of the devastating Asian tsunami in 2004.
The island, which is home to about 75,000 people, was badly hit by the tsunami although communities have since largely been rebuilt.
The 2004 tsunami was triggered by a magnitude 9 undersea earthquake and killed more than 168,000 people in north Sumatra's Aceh province, of which Simeulue is part.
The latest earthquake was felt across Aceh, causing many people to flee their homes, locals said.
One resident, Ahmad Yushadi, told the AP news service: "Everything shook very strongly for more than a minute and I ran along with the others. I heard people screaming in panic."
Indonesia is prone to seismic upheaval due to its location on the so-called Ring of Fire, an arc of volcanoes and fault lines encircling the Pacific Basin.