Stewart said all of the company's 760 Australian employees will continue to be paid and normal customer policies such as gift cards and returns would continue throughout the administration period.
The Australian division has annual sales of approximately A$90 million ($96m).
Topshop was one of the first international fast fashion brands to arrive in Australia in 2011 but has faced increasing competition from the likes of Zara and H&M in recent years.
The company opened its first stand-alone store in New Zealand in March 2015 and has since expanded into Wellington with another two stores planned for Christchurch and Auckland.
Topshop New Zealand said the Kiwi arm of the company was unaffected by the Australian business.
"The franchise for Topshop Topman NZ is an entirely separate entity and shareholding from the Australian business, so their situation doesn't have any affect on our business operations," the company said.
"Unlike the Australian business that has a couple of dozen large format stores in a highly competitive market, our strategy and approach to rolling out the brand in the New Zealand market has been a much slower, considered roll out with currently only 2 stores in key locations."