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Advances in additive manufacturing technologies have shown that bio-additive manufacturing has opened a new frontier in the biomedical field for 3D printing human organs. Despite these advancements, it is significantly challenging to reliably identify damage features, especially embedded defects, using non-contact methods. This research devises a novel method that can reliably assess the damage characteristics without contact by using video-based vibrometry. Vibration signals provide an integrated response of the target structure including geometry changes such as defects in bioprinting. Since the phase shift of the pixel intensity is intrinsically related to any motion captured in the video, the vibration characteristics that reflect surface and embedded defects can be remotely assessed for the entire structure captured in the camera view from a distance without installing several sensors on the structure. In this study, the vibration characteristics of a cube that is manufactured by an extrusion-based bio-printer with pneumatic dispensing are experimentally obtained by using a high-speed camera and phase-based motion estimation technique. The occurrence of damage and its severity are identified by monitoring the change of the vibration characteristics. A finite element model was formulated, and its response characteristics are compared with the experimentally obtained results. Overall, the results of this study reveal promising potential of implementing video vibrometry for effectively verifying the structural integrity of additively manufactured organs after fabrication, which may be the foundational step in the quality testing of bioprints.