The governing body said in a statement that the 31-year-old - who played for Yorkshire in 2015 - would not continue playing in the current T20 series against Sri Lanka.
Team psychologist Dr Michael Lloyd said: “Glenn Maxwell has been experiencing some difficulties with regards to his mental health. As a result, he will spend a short time away from the game.
“Glenn was proactive in identifying these issues and engaging with support staff.”
Maxwell has appeared for Australia in all three forms of the game and has also played for Lancashire County Cricket Club.
He will be replaced in the Australian squad by Darcy Short.