Mr Turnbull says he would offer Australian support to Indonesia when he speaks to President Joko Widodo later in the day.
Chrissy Tiegen and Teresa Palmer tweeted from the Indonesian islands, as they were there at the time of the quake.
Trembling. So long", she wrote, "Oh man.
There are no reports so far of any Australians being killed or injured in the natural disaster that hit Lombok and Bali, despite it being a popular tourist destination for Australians.
Update: A few hours later, it seems the aftershocks are still creating chaos on the islands and for Teigen and Legend.
National Disaster Mitigation Agency spokesman Sutopo Purwo Nugroho said the quake was felt strongly across Lombok and Bali and had damaged houses on both islands.More news: Venezuelan President Nicolas Maduro Survives Apparent Assassination Attempt | Trending
Video showed screaming people running in panic from houses in a Bali neighborhood and vehicles rocking.
The magnitude seven quake hit about 6.46pm Jakarta time (11:46pm), 27 kilometres northeast of northern Lombok at a 15-kilometre depth.
It comes a week after another tremor killed 16 people and injured dozens more on Lombok.
The quake killed at least 82 people on Lombok, about 80.5 kilometres from Bali.
At least 82 people are dead.
The most recent quake struck just nine miles deep and was felt in Denpasar, Bali, where buildings were damaged.More news: Donald Trump taunts basketballer LeBron James in late night Twitter rant
The quake, which struck at a depth of 15km off the north coast of Lombok, prompted a tsunami warning which was later lifted at 8.25pm local time.
"Please go to a place with higher ground, while remaining calm and not panicking", Dwikorita Karnawati, head of the agency for meteorology, climatology and geophysics, told local TV. However, an initial warning of a tsunami with waves of up to half a metre was later withdrawn.
Law and Home Affairs Minister K Shanmugam was among those caught in the 7.0 magnitude quake that struck Indonesian tourist island Lombok yesterday, that killed 39 people.
Bali´s global airport suffered damage to its terminal but the runway was unaffected and operations had returned to normal, disaster agency officials said.
The United States Geological Survey slightly downgraded Sunday's quake after initially calling it 7.0-magnitude.
Famous for their picturesque beaches and mountains, buildings in Lombok and Bali height restrictions keep buildings from exceeding the height of coconut trees, the AP reports.More news: Turkish lira skids past 5 to dollar on USA sanctions move