Defending champion Serena Williams already had withdrawn due to a knee injury.
The siblings beat each other in the final at Flushing Meadows each of the past two years. Venus also won the 2000 title, a year after Serena broke through for her first Grand Slam crown.
The last woman not named Williams to win the U.S. Open was Lindsay Davenport.
Davenport is the top-seeded American woman at No. 3.
This marks the first year since 1994 that one of the top two seeds has not been from the United States.
Clijsters is seeking her first Grand Slam title. Henin-Hardenne won her first at this year's French Open.