The former US Army private turned whistleblower and activist may not make it to Australia with her speaking tour, which is due to commence with a speech at the Sydney Opera House on Sunday and events in Melbourne, Auckland, Wellington and Brisbane.
A spokesman said all non-citizens need to meet certain character requirements before being granted entry to Australia. This was done on the spurious grounds that she fails the Migration Act's "character test" because of a "substantial criminal record".
The minister has the right to deny anyone a visa if they don't pass "the character test", according to the said section 501 of the Migration Act.
Manning was sentenced in 2013 to 35 years in prison for sending more than 700,000 documents, videos and diplomatic cables to WikiLeaks.
The former soldier, freed last year after then United States president Barack Obama commuted her 35-year sentence days before he left office, was due to talk at the Sydney Opera House on Sunday followed by engagements in Melbourne and Brisbane.
"Ms. Manning offers formidable ideas and an insightful perspective which we are hoping to bring to the forefront of Australian dialogue", Think Inc.'s director said in a statement to media about the issue.
Chelsea Manning's New Zealand visit is causing a stir.
Think Inc. said it had received a notice of intention from the government to deny Manning entry.
Amnesty International accused the government of trying to silence Ms Manning.
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Prime Minister Scott Morrison said the decision was for Coleman, who was sworn in as immigration minister on Tuesday.
Following her release from prison, Manning, already a poster-child for free speech, has continued her activism in that area along with promoting data privacy and transgender rights.
"There is great interest in what Ms Manning has to say, evidenced by the fact her upcoming public appearances in Australia are selling quickly".
Chelsea Manning, will run for the US Senate despite her conviction for leaking classified material.
But lobby group the Free Speech Coalition swiftly condemned the calls to bar Ms Manning.
Australia has similar good-character rules to New Zealand.
As Manning had her sentence commuted by Obama rather than being pardoned, her record stands.
Associate Immigration Minister Kris Faafoi's office said he would not comment on individual cases.
"We agree with the reported comments Green Party MP Golriz Ghahraman that Mr Woodhouse's campaign for censorship is offensive".
Chelsea Manning on stage in Berlin in May.
New Zealand's immigration department says it's received an application, which will be looked at by senior officials in the first instance, with a right to appeal to the minister in charge.