Photoabsorption and photoluminescence properties of single and double oxygen vacancy (OV and DOV) defects in quartz-like germanium oxide have been investigated by high-level ab initio calculations. It has been found that photoabsorption for these systems occurs at lower energies as compared to the analogous defects in SiO2. For OV, the lowest electronic excitations with high oscillator strengths have energies of 6.7-7.0 eV, whereas for DOV, the lowest-energy photoabsorption band is calculated to be in the range of 5.5-5.9 eV. Significant geometry relaxation and large Stokes shift are inherent for these excited states and, as a result, their photoluminescence bands are predicted to peak at 3.1-3.3 eV for OV and at 2.6 eV for DOV. The double oxygen vacancy is suggested to be the most suitable candidate for generating bright blue photoluminescence observed experimentally for substoichiometric quartz-like GeO2 nanowires, as the calculated optical properties of DOV are in close agreement with the features found in experiment.