Chris, who was convicted of assaulting his ex-partner pop star Rihanna in 2009, was issued with a "notice of intention to consider refusal", just a day before tickets to his 'One Hell of a Nite' tour were due to go on sale.
"People to whom these notices are issued have 28 days to present material as to why they should be given a visa to enter Australia," Mr Dutton said in a statement.
"Decisions on whether a visa will or will not be issued are made after that timeframe and consideration of the material presented to the Department of Immigration and Border Protection," he added.
The decision to ban the Grammy award-winning performer was mooted by recently appointed Minister of Women Michaelia Cash on Friday as new Prime Minister Malcolm Turnbull unveiled a Aus $100 million (US$70 million) package to address violence in families.
Ms Cash, the former assistant immigration minister, also said that she previously revoked the visa of a "very, very, very wealthy" boxing star, understood to be Floyd Mayweather, who has multiple convictions for assaulting women.
Chris is due to perform in the Australian cities of Perth, Melbourne, Sydney and Brisbane from December 9-16. He previously toured Australia in 2011 and 2012. (Also Read: Chris Brown Hit With Lawsuit Over Nightclub Shooting)