Defending champion Roger Federer will begin the defence of his US Open title on Tuesday when he takes on Ivo Minar of the Czech Republic in the first round.
The world number one Swiss is looking to win back-to-back Grand Slam titles, having clinched his third consecutive Wimbledon crown last month.
World number one Davenport, the second seed and runner-up at the Australian Open and Wimbledon, will play Li Na of China.
American Davenport, the 1998 US Open champion, has not won a Grand Slam title since 2000.
"I will put in a huge effort to try and win a Grand Slam again," she said on the eve of the tournament.
"I've gotten close twice this year and it hasn't happened, so I just keep plugging away in the hope that will happen."
Seventh seed Henin-Hardenne of Belgium, the French Open champion and winner at Flushing Meadows in 2003, faces Zuzana Ondraskova of the Czech Republic.
French third seed Amelie Mauresmo, still searching for her first Grand Slam title, meets Italian Roberta Vinci while last year's runner-up, Russian sixth seed Elena Dementieva, takes on Czech left-hander Lucie Safarova.
In other notable matches, 28th seed Greg Rusedski of Britain meets in-form American James Blake, who won the New Haven Open on Sunday, while another Briton, 12th-seeded Tim Henman, a semi-finalist last year, faces Spaniard Fernando Verdasco.