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NSW could be hit after 8:45am (AEDT) on Sunday, while Queensland could be hit after 8:15am (AEST).
Emergency Management Queensland said residents in coastal areas of the state's south east should keep off beaches and foreshores on Sunday morning when conditions could be rough.
"Advice from the bureau is that there is the possibility of dangerous waves, strong ocean currents and foreshore flooding for several hours tomorrow morning," Acting Deputy Chief Officer Wayne Coutts said in a statement on Saturday night.
"No evacuations are necessary, however we are asking people to avoid their coastal areas.
"Please do not be tempted by curiosity, and consider safety first."
People in NSW are also advised to keep away from the coast.
The NSW government has warned of possible "dangerous waves, strong ocean currents and foreshore flooding for several hours from 8.30am (AEDT)".
"The potential impacts of the tsunami for Australia will become clearer once the tsunami reaches Hawaii," Emergency Services Minister Steve Whan said in a statement.
The NSW State Emergency Service (SES) told AAP late on Saturday that people should stay away from the beach altogether between Broken Bay, north of Sydney, and the Queensland border.
"No fishing, no swimming, no boating," SES spokesman Phil Campbell said.
"There will be people who want to go sightseeing, but urge them not to."
BoM duty forecaster Jake Phillips said the NSW coast north of Broken Bay and up to Queensland's south coast as far as Double Island Point near Brisbane could be affected by strong waves.
But he said there is no concern of land inundation.
"But there is a marine threat and that would include anyone out boating or rock fishermen," he said.
The quake struck off Chile's coast at 3:34am local time (17.34 AEDT) on Saturday, shaking buildings in the capital, where some buildings have collapsed.
For more information about local warnings visit www.bom.gov.au.