NEW YORK–A prominent fund-raiser for President Barack Obama, Hillary Rodham Clinton and other top Democrats left jail Wednesday for his $20 million New York City apartment, where he will remain under house arrest.

Investment banker Hassan Nemazee, 59, left U.S. District Court in Manhattan shortly after noon. He spent one night at the Metropolitan Correctional Center next to the courthouse after his Tuesday arrest on a bank fraud charge. His lawyer, Marc Mukasey, said they had no comment as the two left the courthouse.

Prosecutors say he used “fraudulent and forged” documents to get a $74 million business loan. The chairman and chief executive of New York-based Nemazee Capital Corp. served as national finance chairman for Mrs. Clinton’s presidential campaign in 2008. He raised money for Mr. Obama after her primary defeat.

Mr. Nemazee must wear an electronic monitoring bracelet during his house arrest. He was freed under a $25 million bail package that requires him to pledge his Park Avenue apartment and a Katonah, N.Y., home worth $8 million as collateral within a week. He has $24 million of equity in the properties. He is also banned from using computers or the Internet or getting new cellphones or bank loans.

Mr. Mukasey on Tuesday called the bail terms “draconian” and “staggering.” Assistant U.S. Attorney John Hillebrect said prosecutors have reasons to believe Mr. Nemazee is a flight risk.

According to a complaint filed by the U.S. attorney’s office in Manhattan, Mr. Nemazee provided Citibank with documents showing that he had large amounts of assets in accounts that, in fact, either didn’t exist or had long ago been closed.

Mr. Nemazee on Monday fully repaid the more than $74 million owed to Citibank. If a borrower knowingly provides false information to a bank in order to obtain a loan, he can still be charged with a crime even though he repays the amount owed.

Mr. Nemazee, who has not had to enter a plea because he has not been indicted, faces up to 30 years in prison if he is convicted.