Multiview video plus depth (MVD) is the most popular 3D video format due to its efficient compression and provision for novel view generation enabling the free-viewpoint applications. In addition to color images, MVD format provides depth maps which are exploited to generate intermediate virtual views using the depth image-based rendering (DIBR) techniques. Compression affects the quality of the depth maps which in turn may introduce various structural and textural distortions in the DIBR-synthesized images. Estimation of the compression-related distortion in depth maps is very important for a high-quality 3D experience. The task becomes challenging when the corresponding reference depth maps are unavailable, e.g., when evaluating the quality on the decoder side. In this paper, we present a no-reference quality assessment algorithm to estimate the distortion in the depth maps induced by compression. The proposed algorithm exploits the depth saliency and local statistical characteristics of the depth maps to predict the compression distortion. The proposed ‘depth distortion evaluator’ (DDE) is evaluated on depth videos from standard MVD database compressed with the state-of-the-art high-efficiency video coding at various quality levels. The results demonstrate that DDE can be used to effectively estimate the compression distortion in depth videos.