David Travers, chief executive of the Adelaide-based UCL School of Energy and Resources, wrote to the minister, Chris Bowen, to express concern that changes announced after the recent Knight review of Australian student visas would not apply to his institution.
In the letter - also signed by Terry Buss, head of Carnegie Mellon University's campus in Adelaide - Mr Travers says that "key benefits" of the reforms "appear not to apply to our universities".
This was because of the conditions set by the South Australia state government when both UCL's campus and Carnegie Mellon's Heinz College were set up, meaning that the two institutions were not officially classed as "Australian universities".
As a result, they risked being placed at a competitive disadvantage when the Knight reforms - which include the streamlining of overseas visas and better post-study work rights for foreign students - were implemented, Mr Travers and Dr Buss warn.
However, since sending the letter, Mr Travers said he had been contacted by Mr Bowen's office and been assured that the minister intends to ensure that the two campuses are treated the same as Australian universities.
Mr Travers added that the UCL school, which launched last year, was just six weeks away from graduating its first MSc students and was producing people with the exact skills needed in Australia's booming mining and energy sectors.
"To deny overseas students - who graduate in Australia with a UCL degree - the new two-year post-graduation working visa seemed unfair and we're pleased the minister has stepped in," he added.
British vice-chancellors have warned that Australia's relaxed visa rules will mean heightened competition for universities in the UK, where the government is tightening restrictions on non-European Union students.