The iconic band said in a statement Tuesday they "are deeply sorry and disappointed to announce the postponement of the rest of their 14 ON FIRE tour."
Band members thanked fans "for their support at this difficult time."
The Stones were scheduled to play Wednesday in Perth, Australia, and at other stops this week and next week, including Melbourne and Sydney.
Scott, a noted fashion designer, died Monday in New York City of an apparent suicide.
Tickets holders should keep their tickets, the statement said.