France's Monfils claimed the Swedish title last year when he defeated Finland's Jarkko Nieminen in three sets, but his chance to defend the crown fell by the wayside with a 6-3, 1-6, 6-3 loss to the 24-year-old Rosenholm.
Two seeded players, meanwhile, did better, moving on with first-round victories. Fifth-seeded Feliciano Lopez of Spain, who fired 26 aces in a marathon 7-6 (7-5), 6-7 (4-7), 6-2 win over Frenchman Paul-Henri Mathieu, and No. 7 seed Marcos Baghdatis of Cyprus, who routed Belgian David Goffin 6-4, 6-2.
Other Tuesday winners included wild card Lleyton Hewitt, Romanian qualifier Marius Copil, Estonian Jurgen Zopp, Lithuanian Ricardas Berankis, Colombian Alejandro Falla, Japan's Go Soeda and Ukrainian Sergiy Stakhovsky.