Dominique Strauss-Kahn, 62, was arrested on charges of a criminal sex act, attempted rape and unlawful imprisonment. He was taken off the Air France flight at John F Kennedy International Airport by police officers.
His lawyer, Benjamin Brafman, said he "denies all the charges against him" and planned to plead not guilty.
Yesterday, French politicians urged caution pending further investigation of the allegations. His supporters suggested Strauss-Kahn - seen as a potential rival to Nicolas Sarkozy - could have been set up.
New York police spokesman Paul Browne said a 32-year-old maid filed a sexual assault complaint after fleeing the 1,900-a-night suite at the Sofitel, in Times Square, where the alleged incident took place, at 1pm on Saturday.
Strauss-Kahn appeared to have fled the hotel after the incident, he added.
Mr Browne said: "She told detectives he came out of the bathroom naked, ran down a hallway to the foyer where she was, pulled her into a bedroom and began to sexually assault her.
"She pulled away from him and he dragged her down a hallway into the bathroom, where he engaged in a criminal sexual act, according to her account to detectives. He tried to lock her in the hotel room."
According to New York state law, a criminal sexual act carries a potential sentence of 15 to 20 years, the same as attempted rape. Unlawful imprisonment carries a potential sentence of three to five years.
In a statement yesterday, Strauss-Kahn's wife, Anne Sinclair, said: "I do not believe for a single second the accusations levelled against my husband. I do not doubt his innocence will be established. I appeal for restraint and decency."
Strauss-Kahn has not announced his candidacy for France's presidency, but was widely expected to seek the Socialist Party nomination to run against the conservative, Mr Sarkozy.
His arrest caused shock and disbelief among French politicians yesterday.
"The news last night struck like a thunderbolt," said Socialist leader Martine Aubry.
Franois Bayrou, a centrist opponent of Strauss-Kahn, said: "All this is completely astounding, immensely troubling and distressing."
Far-right leader Marine Le Pen said her rival's presidential hopes had been crushed - she and Strauss-Kahn have been leading Mr Sarkozy in recent opinion polls.
One of Strauss-Kahn's allies, Jean-Marie Le Guen, expressed doubt. "The facts, as they've been reported today, have nothing to do with the Dominique Strauss-Kahn that we know," he said.
In a statement on its website, the IMF declined to comment, saying only that it "remains fully functioning and operational".
It later said that No 2 John Lipsky would step in as acting managing director.
Strauss-Kahn has faced controversy before. In 2008, he apologised for "an error of judgment" after an affair with a female IMF economist who was his subordinate. An inquiry cleared him of harassment and abuse of power, but he was warned against further improper conduct.
Name: Dominique Strauss-Kahn
Age: 62. Born in Neuilly-sur-Seine, France, on 25 April, 1949.
Education: Degrees in law, business administration, political studies and statistics. PhD in economics from the University of Paris.
Family: Wife, Anne Sinclair, and four children by a previous marriage.
Career: Managing director of International Monetary Fund since 2007, winning praise for his handling of the global financial crisis. He was an economics professor, corporate lawyer and minister in France's National Assembly. He was finance minister from 1997-99 and helped France prepare to abandon the franc for the euro. He sought the Socialist Party's nomination for the 2007 presidential elections and is a possible candidate next year.
Quote: "While this incident constituted an error in judgment on my part, for which I take full responsibility, I firmly believe I have not abused my position," he e-mailed IMF staff after an affair with a member of sataff became public in 2008.
In 1990, Strauss-Kahn was already a leading economist