The 39-year-old father-of-two applied to the Federal Court to overturn the decision, with his lawyer Anthony Young arguing the finding his client could flee was a «mere speculative possibility».
Tsvetnenko also sought judicial review of an earlier decision by Canberra magistrate Peter Morrison to issue the arrest warrant.
But Justice Neil McKerracher dismissed the application on Friday, saying bail was only available in special circumstances in extradition cases.
Tsvetnenko’s lawyers had argued his circumstances were special, including medical needs for a spinal condition and the fact he shared care of his young children with his estranged wife, who co-founded fashion label Zhivago.
In happier times, the extroverted glamour couple were snapped on red carpet events and held extravagant parties that some described as tacky.
Their wedding at Peel Manor House saw the bride arrive in a horse-drawn carriage while rapper Snoop Dogg was a guest at Tsvetnenko’s 29th birthday party.
The US Attorney’s Office says the «auto-subscription» scheme Tsvetnenko was allegedly part of a scam which generated more than $US150 million in illegal profits, which the scammers used to fund lavish lifestyles, including expensive holidays, luxury cars and gambling.
Others nabbed in the investigation include Darcy Wedd and Fraser Thompson, who were sentenced to 10 years and five years behind bars, respectively.
Tsvetnenko previously told AAP through a spokeswoman he was not guilty.
He will face an extradition hearing on April 12.