IMF chief Dominique Strauss-Kahn has been remanded in custody at New York's notorious Rikers Island jail on charges of sexual assault.
The judge said Mr Strauss-Kahn, 62, was a flight risk. He was arrested on Saturday after boarding a plane and accused of trying to rape a hotel maid.
He faces seven charges and could be sentenced to up to 25 years in prison.
Mr Strauss-Kahn, who had been seen as a favourite in France's 2012 presidential elections, denies the charges.
His lawyer expressed disappointment at bail being denied, but said his client would be exonerated.
"This battle has just begun," defence lawyer Benjamin Brafman told the court.
Mr Strauss-Kahn had been due to attend an EU finance ministers' meeting in Brussels to discuss financial bail-outs.
The IMF has played a central role in organising rescue packages for the troubled economies of Portugal and Greece.
The BBC's Chris Morris in Brussels says the IMF chief has gained the trust of countries in Europe which are giving financial assistance, and those which are receiving it.
The European Union says the scandal should not affect bail-outs for eurozone countries.
Bail offer denied
Jean-Claude Junker, the Luxembourg prime minister said: "I am very sad and upset. He is a friend of mine... Mr Strauss-Kahn is in the hands of American justice, it's not up to us to comment on this, but it makes me deeply, deeply sad."
French Finance Minister Christine Lagarde described Mr Strauss-Kahn's predicament was "crushing and painful".
The IMF said in a statement that it had been briefed on the charges against its managing director, and that it would "continue to monitor developments".
Prosecutors told the court it was not the first time Mr Strauss-Kahn had been involved in such an incident and argued he had been arrested attempting to flee the country.
Mr Strauss-Kahn's lawyer Benjamin Brafman contested this, saying the defendant had not tried to flee the scene and was actually rushing for a lunch appointment.
He added that Mr Strauss-Kahn later called the hotel to say he was at the airport and had left a mobile phone in his room.
The defence offered to post $1m (£617,000) bail, with Mr Strauss-Kahn to stay at his daughter's address in New York until the next hearing on Friday.
However, Judge Melissa Jackson rejected the application.
"When I hear your client was at JFK airport about to board a flight, that raises some concerns," Ms Jackson said.
The charges relate to an alleged assault at the Times Square Sofitel hotel in New York.
According to the New York Police Department, a 32-year-old maid told officers that when she entered his suite on Saturday afternoon, Mr Strauss-Kahn emerged from the bathroom naked, chased her and sexually assaulted her.
The woman was able to break free and alert the authorities, a NYPD spokesman added.
Later on Saturday Mr Strauss-Kahn was detained on board an Air France flight at New York's John F Kennedy airport minutes before take-off.
The IMF chief underwent medical examinations on Sunday. Police were looking for scratches or any other evidence of his alleged assault.
He was later charged with a "criminal sexual act, unlawful imprisonment and attempted rape". Police say the maid formally identified him in a line-up.
Until he was arrested, Mr Strauss-Kahn was considered a favourite to become the Socialist candidate for the French presidency next year.
Opinion polls gave him a good chance of defeating President Nicolas Sarkozy.
Socialist party president Martine Aubry described his arrest as a "thunderbolt" but called for Mr Strauss-Kahn to be presumed innocent.
Mr Strauss-Kahn's wife, French TV personality Anne Sinclair, has also protested his innocence.
Meanwhile, another allegation against Mr Strauss-Kahn has emerged. A French writer says she may file a complaint for an alleged sexual assault in 2002.
Tristane Banon, 31, says Mr Strauss-Kahn tried to rape her when she went to interview him for a book she was writing.
"We're planning to make a complaint," Ms Banon's lawyer told AFP news agency. Mr Strauss-Kahn's lawyers have so far not responded to the allegation.