The top-ranked Williams sisters Venus and Serena are out injured so Oudin, ranked a career-high 31, will play Russian number two Alla Kudryavtseva in the opening match on Saturday.
Bethanie Mattek-Sands of the U.S. will then square off against world number six Elena Dementieva.
"I played Alla this year at the Australian Open and lost in a tough three-setter," Oudin said on the U.S. Tennis Association website (www.usta.com) on Friday.
"I know both (Kudryavtseva and Dementieva's) games and I am just going to play my game this weekend and hopefully all goes well."
The pair will be reversed for Sunday's singles matches with American and Russian number ones Oudin and Dementieva taking to the court before Mattek-Sands faces Kudryavtseva.
In the doubles, Liezel Huber, the world's top ranked doubles player and Mattek-Sands face Dementieva and Ekaterina Makarova.
(Writing by Steve Keating in Buffalo; editing by Ken Ferris)