Topshop/Topman Australia has been placed into administration due to rising debt levels, putting 760 jobs at risk.
Financial restructuring firm Ferrier Hodgson has been appointed administrator.
The company’s nine stores, 17 concessions and online business will continue to trade while the future of the retailer is discussed with Arcadia.
An Arcadia spokesman said the business is “working with administrators to find a solution”.
The separately owned and operated Australian franchise for the UK retailer opened in 2011.
Myer, Australia’s biggest department store, bought a 25% stake in the Australian arm of the chain in 2015.
Myer’s recent financial results in May revealed that Topshop’s earnings had fallen by $3m (£1.7m), generating a $600,000 (£346,128) loss for Myer.