Automated three-dimensional breast ultrasound (ABUS) is a valuable adjunct to x-ray mammography for breast cancer screening of women with dense breasts. High image quality is essential for proper diagnostics and computer-aided detection. We propose an automated image quality assessment system for ABUS images that detects artifacts at the time of acquisition. Therefore, we study three aspects that can corrupt ABUS images: the nipple position relative to the rest of the breast, the shadow caused by the nipple, and the shape of the breast contour on the image. Image processing and machine learning algorithms are combined to detect these artifacts based on 368 clinical ABUS images that have been rated manually by two experienced clinicians. At a specificity of 0.99, 55% of the images that were rated as low quality are detected by the proposed algorithms. The areas under the ROC curves of the single classifiers are 0.99 for the nipple position, 0.84 for the nipple shadow, and 0.89 for the breast contour shape. The proposed algorithms work fast and reliably, which makes them adequate for online evaluation of image quality during acquisition. The presented concept may be extended to further image modalities and quality aspects.