U.S. captain Mary Joe Fernandez listed Oudin, Bethanie Mattek-Sands and doubles specialist Liezel Huber on her team for the series against Russia.
A fourth U.S. team member is to be selected next week but both Serena and Venus Williams have opted against playing.
The Russians are countering with Elena Dementieva, Anastasia Pavlyuchenkova, Ekaterina Makarova and Alexandra Kudryavtseva.
The matches will be played April 24-25 on an indoor hard court at the Birmingham-Jefferson Convention Complex Arena in Alabama. The winning team advances to the Nov. 6-7 Fed Cup title series against either the Czech Republic or Italy.
The United States has won a record 17 Fed Cup titles but hasn't collected any since 2000. Russia has won four of the last six Fed Cup championships.