Seven search warrants were executed in Melbourne by a joint counter-terrorism team, two months after Prime Minister Tony Abbott warned the threat from home-grown extremists was worsening.
Police said two 18-year-olds were held over terrorism-related offences.
"It is alleged both men were undertaking preparations for planning terrorist acts in Melbourne, which included targeting police officers," Victoria state and federal police said in a joint statement.
"Part of their alleged planning included targeting an ANZAC Day ceremony."
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This year's events have assumed added significance with the day marking a century since the bloody World War I Gallipoli campaign in what is now Turkey.
More than 60,000 Australian and New Zealand troops joined an Allied expeditionary landing on the peninsula in 1915, and 11,500 of them never returned.
The arrests also come just days after Australia began deploying 330 more troops to Iraq for two years to train local soldiers fighting jihadists including the Islamic State group, joining an aerial and special forces contingent in the region.