The tremors were also felt on the nearby resort islands of Lombok and Bali.
One of the dead was reported to be a 5-year-old boy, killed by falling masonry.
Suriyani, a local doctor, told AFP on Monday that most of the injured were being treated at the general hospital in the worst-affected district of Dompu on Sumbawa island.
"We received 34 people injured. Some with slight injuries have gone home already but some 20 people are still under hospital treatment, with broken bones, open wounds and head injuries caused by collapsing walls."
Missed tsunami warning
The Indonesian meteorological agency issued a tsunami warning but it failed to reach the media via the text messaging service usually used to send out alerts.
"There were some problems with the technical equipment and the quake was read as being on land, when actually it was undersea," Ali Imron, an agency official, told AFP.
"Everyone panicked, they were running from their houses, some to the hills"Agung Prasetyo, local police officer
"The threat has already been lifted."
Witnesses said electricity was temporarily cut in some places including a hospital, which was briefly evacuated, Antara state news agency reported.
A worker at the hospital in Raba town about 50km east of Dompu said the tremors caused panic and led to the evacuation of 300 patients, but no casualties were reported in the area.
"All the patients in the hospital rushed to the open air outside, they felt the quake quite strongly," Nining told AFP. "There was panic but I have heard no reports of damage."
Agung Prasetyo, a local police officer, said the ground shook violently for around 30 seconds.
"Everyone panicked, they were running from their houses, some to the hills."
Earlier on Sunday, a separate earthquake rattled residents on the west coast of Sumatra island causing dozens to flee their homes in the earthquake-prone region.
No death or injuries were reported.
The quakes are the latest in a series of powerful tremors and other seismic activity to hit Indonesia.
Indonesia is prone to seismic upheavals due to its location on the so-called Pacific "Ring of Fire", an active belt of volcanoes and fault lines around the Pacific Basin.
In December 2004, a massive earthquake struck off the Sumatran coast, triggering a massive tsunami that killed more than 230,000 people in a dozen countries, including 160,000 people in Indonesia's westernmost province of Aceh.