We present a search for Herschel-PACS counterparts of dust-obscured, high-redshift objects previously selected at submillimeter and millimeter wavelengths in the Great Observatories Origins Deep Survey North field. We detect 22 of 56 submillimeter galaxies (SMGs, 39%) with a signal-to-noise ratio of >=3 at 100 μm down to 3.0 mJy, and/or at 160 μm down to 5.7 mJy. The fraction of SMGs seen at 160 μm is higher than that at 100 μm. About 50% of radio-identified SMGs are associated with PACS sources. We find a trend between the SCUBA/PACS flux ratio and redshift, suggesting that these flux ratios could be used as a coarse redshift indicator. PACS-undetected submillimeter/millimeter selected sources tend to lie at higher redshifts than the PACS-detected ones. A total of 12 sources (21% of our SMG sample) remain unidentified and the fact that they are blank fields at Herschel-PACS and the Very Large Array 20 cm wavelength may imply higher redshifts for them than for the average SMG population (e.g., z>3-4). The Herschel-PACS imaging of these dust-obscured starbursts at high redshifts suggests that their far-infrared spectral energy distributions have significantly different shapes than template libraries of local infrared galaxies.