Bammer lost to Azarenka, a wild card this week, 6-1, 6-3.
In other first-round action, Slovakian Dominika Cibulkova beat Argentine Gisela Dulko 7-6 (7-1), 6-4; Bulgarian Tsvetana Pironkova beat Czech qualifier Klara Zakopalova 6-4, 6-2; and Italian wild card Roberta Vinci defeated Estonian qualifier Kaia Kanepi 6-4, 4-6, 6-0.
Three second-round matches and six first-rounders were either postponed or suspended Tuesday because of rain. Fifth-seeded American Serena Williams was to meet Ukrainian Alona Bondarenko and seventh-seeded Venus Williams was slated to face Aussie Samantha Stosur in the second round, but both bouts were pushed back to Wednesday.
Venus, the Wimbledon champion, returns to action this week after taking a medical leave of absence over the last month.