Monitoring of blood oxygenation, in particular, cerebral venous oxygenation, is necessary for management of a variety of life-threatening conditions. An optoacoustic technique can be used for noninvasive monitoring of blood oxygenation in blood vessels, including large veins. We calculated optoacoustic signals from a cylinder mimicking a blood vessel using a modified Monte Carlo code and analyzed their temporal profiles. The rate of decrease of the integrated optoacoustic signal at different wavelengths of incident near-infrared radiation was related to the effective attenuation coefficient of normally oxygenated venous blood. We obtained good correlation of this parameter with the blood effective attenuation coefficient in a wide spectral range that may be useful in providing an accurate and robust optoacoustic monitoring of blood oxygenation. We also estimated the accuracy of effective attenuation coefficient calculations.