The quake struck at 6.47am local time (11.47pm BST), and its epicentre was located 30.7 miles north-east of the city of Mataram on the island of Lombok, which has a population of 319,000.
Lombok is located close to the popular tourist destination of Bali, and more than 361,000 British holidaymakers visited Indonesia in 2017.
The earthquake was preceded by a moderate size tremor 41 minutes prior.
Local residents also reported feeling aftershocks following the main tremor.
A magnitude 5.5 magnitude earthquake struck near the island of Bali following the initial tremor at 0.06am BST.
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The European-Mediterranean Seismological Centre (EMSC) noted that the estimated population in the affected region was 6.5 million inhabitants.
Authorities have issued a yellow alert, indicating that casualties are possible.
The epicentre of the earthquake was located on land and no tsunami warning has been issued.
Indonesia is prone to seismic activity due to its proximity to the Pacific ‘Ring of Fire’, an series of volcanoes and fault lines in the Pacific Basin.
US model Chrissy Teigen, who is holidaying in Bali with her husband John Legend, commented on the earthquake, saying: “Oh my. Long earthquake here in Bali.”
Magnitude 6.4 earthquakes are strong enough to cause damage to property, but their impact depends on their location and the density of populations in the vicinity.
The Hualien earthquake, which hit Taiwan in February 2018 and had a magnitude of 6.4, killed 17 people and injured another 285.
The Foreign Office issued advice on what to do in the event of an earthquake in Indonesia.
They said: “If a major earthquake or landslide occurs close to shore, you should follow the instructions of local authorities, bearing in mind that a tsunami could arrive within minutes.
“The Indonesia Tsunami Early Warning Centre issues tsunami warnings when a potential tsunami with significant impact is imminent or expected.”