Many regions elsewhere in New South Wales (NSW) have had poor visibility.
Authorities said the storm was driven by strong winds picking up dry soil.
Paramedics said dozens of people had reported breathing or asthma difficulties on Thursday, but the number affected by dust was not immediately clear.
In Sydney, the dust darkened skies and caused “hazardous” air quality readings in some suburbs.
One resident in Broken Hill, a town 1,100km west of Sydney, said the dust had lingered for hours on Wednesday.
“You walked outside and it was in your eyes and it was just a gritty feeling,” Matt Whitelum told the BBC.
“The winds were also so strong that you had to hold the car door open or it would just slam back into your face.”
The dust storm is moving through #NSW. This photo taken in the Blue Mountains moments ago by @RFSCommissioner. Expected to reach the coast over the coming hours. #dust#drought2018pic.twitter.com/kzxmQYek3f
— NSW RFS (@NSWRFS) November 21, 2018
The Sydney dust storm has drawn comparisons to a more intense event which shrouded the city in 2009.
That dust storm left hundreds of people suffering from breathing difficulties, and forced the grounding of flights.