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 (39%) with a SNR of >=3 at 100 micron down to 3.0 mJy, and/or at 160 micron down to 5.7 mJy. The fraction of SMGs seen at 160 micron is higher than that at 100 micron. 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 submm/mm 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 VLA 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.