Rustam Pakaya, the head of Indonesia's health ministry crisis centre told reporters that 38 people had been hospitalised with injuries caused by the quake.
He also said that several buildings have been damaged but that the situation was "under control" and that a team of health workers had been sent to the area.
Sumbawa is located east of the resort islands of Lombok and Bali.
Pakaya said that residents in Bima city had felt "strong shaking" and there were reports that "walls of houses have collapsed".
Series of quakes
The US Pacific Tsunami Warning Centre said there was no tsunami threat from the quake, but it does come after a series of earthquakes and aftershocks in Indonesia.
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| September's earthquake in Padang left at least 1,100 people dead [Reuters] |
A 7.6 magnitude undersea earthquake struck in September on the island of Sumatra, killing at least 1,100 people.
The quake occurred around 50km from the city of Padang, flattening hundreds of buildings.
Dozens of aftershocks followed, as did a 6.8 magnitude earthquake that struck the following day, about 225km southeast of Padang, causing widespread panic and badly damaging houses but causing no casualties.
Indonesia straddles some of the most seismically active fault lines in the world, part of the so-called Ring of Fire that encircles the Pacific.
In late 2004 a massive magnitude 9.2 undersea quake off northern Sumatra triggered the Indian Ocean tsunami that killed more than 220,000 people in Indonesia, Thailand, Sri Lanka and India among other countries.