A chemical engineering student spent millions on handbags and luxury goods after a bank provided the funds in error, a Sydney court has heard.

Christine Jiaxin Lee, 21, was arrested at Sydney Airport on Wednesday night, Australian media reported.

Waverley Local Court has heard she was trying to board a flight to Malaysia using an emergency issued Malaysian passport.

According to the police prosecutor, the money was accessed through an overdraft facility, mistakenly attached to a Westpac savings account.

It is alleged she obtained $4.6 million (four million euros) fraudulently, $3.3 million (2.8 million euros) of which has not been recovered.

In addition to a charge of obtaining financial advantage by deception, she was also charged with knowingly dealing with proceeds of crime.

The magistrate appeared to suggest the second charge might be more difficult to prove.

"It's not proceeds of crime, it's money we all dream about," Ms Stapleton said.

The court heard the woman has completed three years of a chemical engineering degree and has deferred her fourth year of study.

She has been living in Australia for the past five years and in March, a warrant was issued for her arrest.

Ms Stapleton agreed to grant the woman bail on a number of conditions, including that she report to police twice a day.

The case will return to court at the Downing Centre on June 21.