Muller was dropped in straight sets by Alla Kudryavtseva, 6-3, 6-4, on the second day of the inaugural Barcelona event.
Four top eight seeds advanced with wins Tuesday. Fourth-seeded Kaia Kanepi stopped Karin Knapp, 6-3, 7-6 (9-7); No. 5 Lourdes Dominguez Lino took out Greta Arn, 6-2, 6-4; seventh-seeded Virginie Razzano took a 7-6 (8-6), 3-6, 6-0 decision from Julia Schruff; and No. 8 Flavia Pennetta beat Conchita Martinez, 6-2, 6-2.
Szavay advances to a second-round match with top-seeded Francesca Schiavone.
2014: The Year in Music [PHOTOS]