The New York Post said he was arrested in the first class cabin of an Air France aircraft that was two minutes away from taking off from New York’s Kennedy Airport.
Quoting “police sources”, the newspaper said three Port Authority detectives boarded the Paris-bound jet to arrest the 62-year-old Frenchman.
Strauss-Kahn, a leader of France’s Socialist Party, is the leading rival to President Nicolas Sarkozy in the 2012 election.
Mr Strauss-Khan was reported to have been taken to the New York Police Department’s Midtown South precinct.
The case is said to involve allegations of a sexual assault against a Manhattan hotel maid during an incident on Saturday afternoon. It is being investigated by the New York police’s Special Victims Unit.
It is currently unclear whether Strauss-Khan will have to postpone a planned meeting in Berlin on Sunday with the German chancellor Angela Merkel.
In 2008, Strauss-Khan publicly admitted to “an error of judgment” for having an affair with an IMF subordinate.
In 2006 Strauss-Kahn lost the Socialist Party nomination to Segolene Royal, who was in turn defeated by Sarkozy in the French presidential election.
Strauss-Kahn is married to New York-born Anne Sinclair, a leading French TV journalist.
He was France’s Minister of Economy and Finance from 1997 to 1999