The 27-year-old was rushed back into the extended squad last week by interim coach Tim Walsh just days after arriving back from the Rugby World Cup in England, where the Wallabies reached the final.
However, he missed out on the final selection for the Oceania event in west Auckland this weekend, with Walsh saying the Fiji-born flyer still needed time to adjust to the cut-down version of the game.
"It's a bit different for Henry coming in so quickly to understand sevens and the policies in the structures which he run," Walsh said in a statement.
"Its just a great opportunity for Henry to understand sevens and get a look in."
Even without Speight, Walsh's side should prove too strong for the other teams in the tournament with fellow World Sevens Series regulars Samoa providing their biggest threat.
"The Samoans have always given us trouble and Tonga has been tough opposition over the last couple of years," Australia captain Ed Jenkins said.
"That's a tough ask in hand, but we have done the hard work so we should be going into this tournament quite confident."
Jenkins' side won a tournament last month on Australia's Central Coast north of Sydney, which included club teams from sevens powerhouse Fiji and national development teams from New Zealand, Canada and the United States.
"It gives the boys a lot of confidence coming into this tournament," he added. "We have got some good preparation behind us and now we just need to put it into action."
Fiji and New Zealand are not present having already qualified for the men's tournament in Rio after finishing in the top four of the world series, while the Australian and New Zealand women's teams have also qualified.
Pacific Games champions Fiji are expected to top the women's competition this weekend.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
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