"We have a passionate conviction to be back here on the Gold Coast."
In a statement posted on Twitter, the Australian director said that "this is not the moment to be resuming production on the film", which is being shot on the Gold Coast.
"Please know that this is in now way a reflection our commitment to making the movie here in Queensland. In fact we are not even taking our sets down, simply locking up the creative space over the next few days," Luhrmann's statement reads.
“I have spoken to the premier Annastacia Palaszczuk, and we all agree that right now, this is the time for people all over the world, from all walks of life, to be at home indoors, with their loved ones (washing our hands five time a day).
"All going well we have a passionate conviction to be back here on the Gold Coast, picking up where we left off as soon as the time is right.”
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Hanks plays Colonel Tom Parker, Presley's manager, in the film, while fellow US actor Austin Butler stars as the late music icon.
Other names to appear in the biopic include Maggie Gyllenhaal, Rufus Sewell, UK singer Yola and Australia's own Olivia DeJonge.
The film is scheduled for release next year.