Karzai and his entourage, which includes senior ministers, will visit Canada after the UN meeting in New York and then return to Washington for a state visit.
Karzai is due to meet U.S. President George W. Bush and Pakistan President Pervez Musharraf during the trip.
In Afghanistan, a top NATO general said on September 17 that the alliance's anti-Taliban offensive in southern Afghanistan has been "successfully completed."
British Lieutenant General David Richard, the head of the 20,000-strong NATO-led force, called the two week-long operation a "significant success," with the insurgents forced to abandon many of their positions.
Reconstruction and development efforts will begin shortly in three parts of the south, Richard said.
In other news, police say a suicide attack near a convoy of NATO-led troops in the southern city of Kandahar killed one person and wounded five.
No members of the international coalition were injured.