Half the roster for the American squad is changed from the team that beat Slovenia, 4-1, in February.
Rubin is coming off a first-round loss to France's Marion Bartoli at Wimbledon two weeks ago. She has played sparingly this season due to injuries.
The 24th-ranked Rubin takes on Barbara Schwartz in the first match Saturday and Lisa Raymond squares off against Barbara Schett.
Raymond will play doubles with Hall of Famer Martina Navratilova.
In other quarterfinals, it will be Russia at Argentina, France at Italy and Belgium at Spain.