For clinical optoacoustic imaging, linear probes are preferably used because they allow versatile imaging of the human body with real-time display and free-hand probe guidance. The two-dimensional (2-D) optoacoustic image obtained with this type of probe is generally interpreted as a 2-D cross-section of the tissue just as is common in echo ultrasound. We demonstrate in three-dimensional simulations, phantom experiments, and in vivo mouse experiments that for vascular imaging this interpretation is often inaccurate. The cylindrical blood vessels emit anisotropic acoustic transients, which can be sensitively detected only if the direction of acoustic radiation coincides with the probe aperture. Our results reveal for this reason that the signal amplitude of different blood vessels may differ even if the vessels have the same diameter and initial pressure distribution but different orientation relative to the imaging plane. This has important implications for the image interpretation, for the probe guidance technique, and especially in cases when a quantitative reconstruction of the optical tissue properties is required.