Mr Strauss-Kahn, 62, was taken off an Air France plane at JFK airport just minutes before it left for Paris. Police say he faces three charges, including attempted rape. His lawyer told Reuters he would plead not guilty.
The married former French finance minister is also considered a possible Socialist candidate for the presidency. The BBC’s Hugh Schofield, in Paris, says Mr Strauss-Kahn has been riding high in the polls and was seen as having a genuine chance of beating President Nicolas Sarkozy.
However, this incident is likely to kill off any chance of electoral success, Hugh Schofield says.
Mr Strauss-Kahn is expected to appear before a New York state court later on Sunday, Reuters reports. He had been scheduled to meet German Chancellor Angela Merkel on Sunday, but that meeting has now been cancelled, reports say.
On Monday he had planned to attend a meeting of European Union finance ministers in Brussels on Monday to discuss the bailouts of Portugal and Greece. Correspondents say his detention is likely to complicate ongoing efforts to stabilise the finances of struggling eurozone member states.
In a brief statement posted online on Sunday, an IMF spokeswoman acknowledged Mr Strauss-Kahn’s arrest and said the organisation would not comment on the case. “The IMF remains fully functioning and operational,” she added.