Gupta, also a former global managing director of the consulting firm McKinsey & Co, had asked the country's highest court for permission to stay free during his appeal, after the 2nd U.S. Circuit Court of Appeals in Manhattan on May 30 denied him the same request.
Justice Ruth Bader Ginsburg, who handles emergency applications from the 2nd Circuit, on Wednesday denied Gupta's request to stay out of prison.
The full 2nd Circuit has yet to decide whether to rehear Gupta's appeal of his conviction, which a three-judge panel of that court upheld on March 25.
Gary Naftalis, a partner at Kramer Levin Naftalis & Frankel who represented Gupta, declined to comment. Seth Waxman, a WilmerHale partner and former U.S. solicitor general, is also among Gupta's lawyers.
Gupta, 65, is the highest-ranking corporate official to be convicted in the government's multi-year probe of insider trading in the hedge fund industry.
A Manhattan federal jury in June 2012 convicted him of passing tips about Goldman, including news about its results and a $5 billion investment from Warren Buffett, to his friend Raj Rajaratnam, founder of the Galleon Group hedge fund firm.
In appealing his conviction, Gupta is challenging the use of wiretap evidence and the jury instructions.
Gupta's lawyers have said the appeal is likely to result in a reversal of the conviction and a new trial.
The trial judge, Jed Rakoff, has agreed to recommend that Gupta be assigned to a medium-security prison in Otisville, New York, about 70 miles (113 km) northwest of New York City.
Rajaratnam is serving an 11-year prison term after his 2011 insider trading conviction, in a case also built with wiretap evidence. He is appealing his conviction to the Supreme Court.