The 47-year-old was criticised for his cost-cutting measures, including asking 80% of staff to take a pay cut.
He was appointed in October 2018 following James Sutherland's 17-year tenure.
Englishman Nick Hockley, the chief executive of the T20 World Cup, has replaced Roberts on an interim basis.
Cricket Australia said a wider "operational reset" at the governing body will be announced this week.
Roberts is the third CEO of a major Australian sport to depart in the past two months after the National Rugby League's Todd Greenberg and Rugby Australia's Raelene Castle stood down in April.